Verfügbarkeit: Cyclic homology in non-commutative geometry

Cyclic homology in non-commutative geometry:

Gespeichert in:

Bibliographische Detailangaben
Hauptverfasser:	Cuntz, Joachim 1948- (VerfasserIn), Skandalis, Georges (VerfasserIn), Tsygan, Boris (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Berlin [u.a.] Springer 2004
Schriftenreihe:	Encyclopaedia of mathematical sciences 121
Schlagworte:	Nichtkommutative Geometrie K-Theorie Zyklische Homologie
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	X, 137 S.
ISBN:	3540404694

Internformat

MARC


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245	1	0	\|a Cyclic homology in non-commutative geometry \|c Joachim Cuntz ; Georges Skandalis ; Boris Tsygan
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Datensatz im Suchindex

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adam_text	CONTENTS CYCLIC THEORY, BIVARIANT K -THEORY AND THE BIVARIANT CHERN-CONNES CHARACTER JOACHIM CUNTZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 CYCLIC HOMOLOGY BORIS TSYGAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 NONCOMMUTATIVE GEOMETRY, THE TRANSVERSE SIGNATURE OPERATOR, AND HOPF ALGEBRAS [AFTER A. CONNES AND H. MOSCOVICI] GEORGES SKANDALIS (TRANSLATED BY RAPHA¨ EL PONGE AND NICK WRIGHT) . . . . . 115 INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 CYCLIC THEORY, BIVARIANT K -THEORY AND THE BIVARIANT CHERN-CONNES CHARACTER * JOACHIM CUNTZ 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 CYCLIC THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1 PRELIMINARIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 CYCLIC HOMOLOGY VIA THE CYCLIC BICOMPLEX . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 OPERATORS ON DIFFERENTIAL FORMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4 THE PERIODIC THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.5 CYCLIC HOMOLOGY VIA THE X -COMPLEX . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.6 CYCLIC HOMOLOGY AS NON-COMMUTATIVE DE RHAM THEORY . . . . . . . . . . . 27 2.7 HOMOTOPY INVARIANCE FOR CYCLIC THEORY. . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.8 MORITA INVARIANCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.9 EXCISION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.10 CHERN CHARACTER FOR K -THEORY ELEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . 34 3 CYCLIC THEORY FOR LOCALLY CONVEX ALGEBRAS . . . . . . . . . . . . . . . . . 36 3.1 GENERAL MODIFICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.2 DE RHAM THEORY FOR DIFFERENTIABLE MANIFOLDS . . . . . . . . . . . . . . . . . . . . 38 3.3 CYCLIC HOMOLOGY FOR SCHATTEN IDEALS. . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.4 CYCLIC COCYCLES ASSOCIATED WITH FREDHOLM MODULES . . . . . . . . . . . . . . . 40 4 BIVARIANT K -THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.1 BIVARIANT K -THEORY FOR LOCALLY CONVEX ALGEBRAS . . . . . . . . . . . . . . . . . . 43 4.2 THE BIVARIANT CHERN-CONNES CHARACTER . . . . . . . . . . . . . . . . . . . . . . . . . 48 5 INFINITE-DIMENSIONAL CYCLIC THEORIES . . . . . . . . . . . . . . . . . . . . . . . 51 5.1 ENTIRE CYCLIC COHOMOLOGY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 5.2 LOCAL CYCLIC COHOMOLOGY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 * RESEARCH SUPPORTED BY THE DEUTSCHE FORSCHUNGSGEMEINSCHAFT 2 JOACHIM CUNTZ A LOCALLY CONVEX ALGEBRAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 A.1 ALGEBRAS OF DIFFERENTIABLE FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 A.2 THE SMOOTH TENSOR ALGEBRA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 A.3 THE FREE PRODUCT OF TWO M -ALGEBRAS . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 A.4 THE ALGEBRA OF SMOOTH COMPACT OPERATORS . . . . . . . . . . . . . . . . . . . . . . 64 A.5 THE SCHATTEN IDEALS * P ( H ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 A.6 THE SMOOTH TOEPLITZ ALGEBRA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 B STANDARD EXTENSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 B.1 THE SUSPENSION EXTENSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 B.2 THE FREE EXTENSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 B.3 THE UNIVERSAL TWO-FOLD TRIVIAL EXTENSION. . . . . . . . . . . . . . . . . . . . . . . . . 67 B.4 THE TOEPLITZ EXTENSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 1 INTRODUCTION THE TWO FUNDAMENTAL MACHINES OF NON-COMMUTATIVE GEOMETRY ARE (BIVARI- ANT) TOPOLOGICAL K -THEORY AND CYCLIC HOMOLOGY. IN THE PRESENT CONTRIBUTION WE DESCRIBE THESE TWO THEORIES AND THEIR CONNECTIONS. CYCLIC THEORY CAN BE VIEWED AS A FAR REACHING GENERALIZATION OF THE CLASSICAL DE RHAM COHOMOLOGY, WHILE BIVARIANT K -THEORY INCLUDES THE TOPOLOGICAL K -THEORY OF ATIYAH-HIRZEBRUCH AS A SPECIAL CASE. THE CLASSICAL COMMUTATIVE THEORIES CAN BE EXTENDED TO A DEGREE OF GENERAL- ITY WHICH IS QUITE STRIKING. IT IS IMPORTANT TO NOTE HOWEVER THAT THIS EXTENSION IS BY NO MEANS SIMPLY BASED ON GENERALIZATIONS OF THE EXISTING CLASSICAL METH- ODS. THE CONSTRUCTIONS ARE QUITE DIFFERENT AND GIVE, IN THE COMMUTATIVE CASE, A NEW APPROACH AND AN UNEXPECTED INTERPRETATION OF THE WELL-KNOWN CLASSICAL THEORIES. ONE ASPECT IS THAT SOME OF THE PROPERTIES OF THE TWO THEORIES BECOME VISIBLE ONLY IN THE NON-COMMUTATIVE CATEGORY. FOR INSTANCE, BOTH THEORIES HAVE CERTAIN UNIVERSALITY PROPERTIES IN THIS SETTING. BIVARIANT K -THEORY HAS FIRST BEEN DEFINED AND DEVELOPED BY KASPAROV ON THE CATEGORY OF C * -ALGEBRAS (POSSIBLY WITH THE ACTION OF A LOCALLY COMPACT GROUP) THEREBY UNIFYING AND DECISIVELY EXTENDING PREVIOUS WORK BY ATIYAH- HIRZEBRUCH, BROWN-DOUGLAS-FILLMORE AND OTHERS. KASPAROV ALSO APPLIED HIS BIVARIANT THEORY TO OBTAIN STRIKING POSITIVE RESULTS ON THE NOVIKOV CONJEC- TURE. VERY RECENTLY [13], IT WAS DISCOVERED THAT IN FACT, BIVARIANT TOPOLOGICAL K -THEORIES CAN BE DEFINED ON A WIDE VARIETY OF TOPOLOGICAL ALGEBRAS RANG- ING FROM RATHER GENERAL LOCALLY CONVEX ALGEBRAS TO E.G. BANACH ALGEBRAS OR C * -ALGEBRAS (IN FACT, EVEN ALGEBRAS WITHOUT A SPECIFIED TOPOLOGY CAN BE COV- ERED TO SOME EXTENT). IF E IS THE COVARIANT FUNCTOR FROM SUCH A CATEGORY C OF ALGEBRAS GIVEN BY TOPOLOGICAL K -THEORY OR ALSO BY PERIODIC CYCLIC HOMOLOGY, THEN IT POSSESSES THE FOLLOWING THREE FUNDAMENTAL PROPERTIES: CYCLIC HOMOLOGY * BORIS TSYGAN 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 2 HOCHSCHILD AND CYCLIC HOMOLOGY OF ALGEBRAS . . . . . . . . . . . . . . . 76 2.1 HOMOLOGY OF DIFFERENTIAL GRADED ALGEBRAS . . . . . . . . . . . . . . . . . . . . . . . 78 2.2 THE HOCHSCHILD COCHAIN COMPLEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 2.3 PRODUCTS ON HOCHSCHILD AND CYCLIC COMPLEXES . . . . . . . . . . . . . . . . . . . 80 2.4 PAIRINGS BETWEEN CHAINS AND COCHAINS . . . . . . . . . . . . . . . . . . . . . . . . . . 82 2.5 A * STRUCTURE ON C * ( C * ( A )) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 3 THE CYCLIC COMPLEX C * * . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 3.1 DEFINITION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 3.2 THE REDUCED CYCLIC COMPLEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 3.3 RELATION TO LIE ALGEBRA HOMOLOGY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 3.4 THE CONNECTING MORPHISM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 3.5 OTHER OPERATIONS ON THE CYCLIC COMPLEXES . . . . . . . . . . . . . . . . . . . . . . . 90 3.6 RIGIDITY OF PERIODIC CYCLIC HOMOLOGY . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4 NONCOMMUTATIVE DIFFERENTIAL CALCULUS . . . . . . . . . . . . . . . . . . . . . 92 4.1 GERSTENHABER ALGEBRAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.2 THE GERSTENHABER ALGEBRA V * ( A ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.3 CALCULI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.4 THE CALCULUS CALC( A ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4.5 ENVELOPING ALGEBRA OF A GERSTENHABER ALGEBRA . . . . . . . . . . . . . . . . . . . 95 4.6 RELATION TO THE A * STRUCTURE ON CHAINS . . . . . . . . . . . . . . . . . . . . . . . . 95 5 CYCLIC OBJECTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 5.1 SIMPLICIAL OBJECTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 5.2 CYCLIC OBJECTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 * SUPPORTED IN PART BY NSF GRANT. 74 BORIS TSYGAN 6 EXAMPLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 6.1 SMOOTH FUNCTIONS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 6.2 COMMUTATIVE ALGEBRAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 6.3 RINGS OF DIFFERENTIAL OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 6.4 RINGS OF COMPLETE SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6.5 RINGS OF PSEUDODIFFERENTIAL OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6.6 NONCOMMUTATIVE TORI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 6.7 DEFORMATION QUANTIZATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 6.8 THE BRYLINSKI SPECTRAL SEQUENCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 6.9 DEFORMATION QUANTIZATION: GENERAL CASE . . . . . . . . . . . . . . . . . . . . . . . . . 105 6.10 GROUP RINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 7 INDEX THEOREMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 7.1 INDEX THEOREM FOR DEFORMATIONS OF SYMPLECTIC STRUCTURES . . . . . . . . . . 107 7.2 INDEX THEOREM FOR HOLOMORPHIC SYMPLECTIC DEFORMATIONS . . . . . . . . . . 108 7.3 GENERAL INDEX THEOREM FOR DEFORMATIONS . . . . . . . . . . . . . . . . . . . . . . . . 108 8 RIEMANN-ROCH THEOREM FOR D-MODULES . . . . . . . . . . . . . . . . . . . . 109 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 1 INTRODUCTION MANY GEOMETRIC OBJECTS ASSOCIATED TO A MANIFOLD M CAN BE EXPRESSED IN TERMS OF AN APPROPRIATE ALGEBRA A OF FUNCTIONS ON M (MEASURABLE, CONTIN- UOUS, SMOOTH, HOLOMORPHIC, ALGEBRAIC, . . . ). VERY OFTEN THOSE OBJECTS CAN BE DEFINED IN A WAY THAT IS APPLICABLE TO ANY ALGEBRA A , COMMUTATIVE OR NOT. STUDY OF ASSOCIATIVE ALGEBRAS BY MEANS OF SUCH OBJECTS OF GEOMETRIC ORIGIN IS THE SUBJECT OF NONCOMMUTATIVE GEOMETRY [12,48]. THE HOCHSCHILD AND CYCLIC (CO)HOMOLOGY THEORY IS THE PART OF NONCOMMUTATIVE GEOMETRY WHICH GENER- ALIZES THE CLASSICAL DIFFERENTIAL AND INTEGRAL CALCULUS. THE GEOMETRIC OBJECTS BEING GENERALIZED TO THE NONCOMMUTATIVE SETTING ARE DIFFERENTIAL FORMS, DEN- SITIES, MULTIVECTOR FIELDS, ETC. IN OUR EXPOSITION, THE PRIMARY OBJECT IS THE NEGATIVE CYCLIC COMPLEX CC * * ( A ). OTHER COMPLEXES, NAMELY THE HOCHSCHILD CHAIN COMPLEX C * ( A ), THE PERIODIC CYCLIC COMPLEX CC PER * ( A ), AND THE CYCLIC COMPLEX CC * ( A ), ARE DE- FINED AS RESULTS OF SOME NATURAL PROCEDURE APPLIED TO CC * * ( A ). THE CYCLIC HOMOLOGY IS THE HOMOLOGY OF THE CYCLIC COMPLEX CC * ( A ). IT WAS ORIGINALLY DE- FINED USING ANOTHER STANDARD COMPLEX WHICH WE DENOTE BY C * * ( A ). THE STUDY OF THIS LATTER COMPLEX HAS A DISTINCTLY DIFFERENT FLAVOR, MAINLY COMING FROM THE FACT THAT IT IS RELATED TO THE LIE ALGEBRA HOMOLOGY. THE ABOVE COMPLEXES ARE NONCOMMUTATIVE VERSIONS OF THE SPACE OF DIFFER- ENTIAL FORMS (THE HOCHSCHILD CHAIN COMPLEX) AND OF THE DE RHAM COMPLEX. ONE ALSO DEFINES THE HOCHSCHILD COCHAIN COMPLEX C * ( A, A ) WHICH IS A NON- COMMUTATIVE ANALOGUE OF THE SPACE OF MULTIVECTOR FIELDS. NONCOMMUTATIVE GEOMETRY, THE TRANSVERSE SIGNATURE OPERATOR, AND HOPF ALGEBRAS [AFTER A. CONNES AND H. MOSCOVICI] * GEORGES SKANDALIS (TRANSLATED BY RAPHA¨ EL PONGE AND NICK WRIGHT) 1 PRELIMINARIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 1.1 COMPLEX POWERS OF PSEUDODIFFERENTIAL OPERATORS; THE WODZICKI-GUILLEMIN RESIDUE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 1.2 CYCLIC COHOMOLOGY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 1.3 K -HOMOLOGY; P -SUMMABLE CYCLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 2 THE LOCAL INDEX FORMULA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 3 THE DIFF-INVARIANT SIGNATURE OPERATOR . . . . . . . . . . . . . . . . . . . . 122 3.1 THE HILBERT SPACE H AND THE ALGEBRA A . . . . . . . . . . . . . . . . . . . . . . . . 123 3.2 THE VERTICAL PART OF THE SIGNATURE OPERATOR. . . . . . . . . . . . . . . . . . . . . . 124 3.3 THE HORIZONTAL PART OF THE SIGNATURE OPERATOR . . . . . . . . . . . . . . . . . . . 124 3.4 THE SPECTRAL TRIPLE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 4 THE TRANSVERSE HOPF ALGEBRA . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 4.1 MATCHED PAIRS OF GROUPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 4.2 THE HOPF ALGEBRA H N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 4.3 CYCLIC COHOMOLOGY OF HOPF ALGEBRAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 4.4 THE CLASSIFYING MAP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 4.5 CYCLIC COHOMOLOGY OF THE HOPF ALGEBRA H N . . . . . . . . . . . . . . . . . . . . . . 129 4.6 THE CYCLIC COCYCLE * . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 4.7 CALCULATION OF * . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 4.8 A VARIANT OF THE HOPF ALGEBRA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 * ORIGINALLY PUBLISHED AS G´ EOM´ ETRIE NON COMMUTATIVE, OP´ ERATEUR DE SIGNATURE TRANSVERSE ET ALG` EBRES DE HOPF IN S´ EMINAIRE BOURBAKI, 53 ` EME ANN´ EE, 2000*2001, NO. 892
any_adam_object	1
author	Cuntz, Joachim 1948- Skandalis, Georges Tsygan, Boris
author_GND	(DE-588)137444311
author_facet	Cuntz, Joachim 1948- Skandalis, Georges Tsygan, Boris
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author_sort	Cuntz, Joachim 1948-
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discipline	Mathematik
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id	DE-604.BV017430925
illustrated	Not Illustrated
indexdate	2024-07-09T19:17:56Z
institution	BVB
isbn	3540404694
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-010502735
oclc_num	441629553
open_access_boolean
owner	DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-11 DE-188 DE-384
owner_facet	DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-11 DE-188 DE-384
physical	X, 137 S.
publishDate	2004
publishDateSearch	2004
publishDateSort	2004
publisher	Springer
record_format	marc
series	Encyclopaedia of mathematical sciences
series2	Encyclopaedia of mathematical sciences Encyclopaedia of mathematical sciences / Operator algebras and non-commutative geometry
spelling	Cuntz, Joachim 1948- Verfasser (DE-588)137444311 aut Cyclic homology in non-commutative geometry Joachim Cuntz ; Georges Skandalis ; Boris Tsygan Berlin [u.a.] Springer 2004 X, 137 S. txt rdacontent n rdamedia nc rdacarrier Encyclopaedia of mathematical sciences 121 Encyclopaedia of mathematical sciences / Operator algebras and non-commutative geometry 2 Nichtkommutative Geometrie (DE-588)4171742-9 gnd rswk-swf K-Theorie (DE-588)4033335-8 gnd rswk-swf Zyklische Homologie (DE-588)4269326-3 gnd rswk-swf Zyklische Homologie (DE-588)4269326-3 s K-Theorie (DE-588)4033335-8 s Nichtkommutative Geometrie (DE-588)4171742-9 s DE-604 Skandalis, Georges Verfasser aut Tsygan, Boris Verfasser aut Operator algebras and non-commutative geometry Encyclopaedia of mathematical sciences 2 (DE-604)BV014111511 2 Encyclopaedia of mathematical sciences 121 (DE-604)BV024126459 121 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010502735&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Cuntz, Joachim 1948- Skandalis, Georges Tsygan, Boris Cyclic homology in non-commutative geometry Encyclopaedia of mathematical sciences Nichtkommutative Geometrie (DE-588)4171742-9 gnd K-Theorie (DE-588)4033335-8 gnd Zyklische Homologie (DE-588)4269326-3 gnd
subject_GND	(DE-588)4171742-9 (DE-588)4033335-8 (DE-588)4269326-3
title	Cyclic homology in non-commutative geometry
title_auth	Cyclic homology in non-commutative geometry
title_exact_search	Cyclic homology in non-commutative geometry
title_full	Cyclic homology in non-commutative geometry Joachim Cuntz ; Georges Skandalis ; Boris Tsygan
title_fullStr	Cyclic homology in non-commutative geometry Joachim Cuntz ; Georges Skandalis ; Boris Tsygan
title_full_unstemmed	Cyclic homology in non-commutative geometry Joachim Cuntz ; Georges Skandalis ; Boris Tsygan
title_short	Cyclic homology in non-commutative geometry
title_sort	cyclic homology in non commutative geometry
topic	Nichtkommutative Geometrie (DE-588)4171742-9 gnd K-Theorie (DE-588)4033335-8 gnd Zyklische Homologie (DE-588)4269326-3 gnd
topic_facet	Nichtkommutative Geometrie K-Theorie Zyklische Homologie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010502735&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV014111511 (DE-604)BV024126459
work_keys_str_mv	AT cuntzjoachim cyclichomologyinnoncommutativegeometry AT skandalisgeorges cyclichomologyinnoncommutativegeometry AT tsyganboris cyclichomologyinnoncommutativegeometry

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