Lectures on functor homology:
Gespeichert in:
| Weitere Verfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English French |
| Veröffentlicht: |
Cham
Birkhäuser
[2015]
Cham Springer |
| Schriftenreihe: | Progress in mathematics
volume 311 |
| Schlagworte: | |
| Online-Zugang: | BTU01 TUM01 UBM01 UBT01 UBW01 UEI01 UEI01 UPA01 Volltext Inhaltsverzeichnis Abstract |
| Beschreibung: | 1 Online-Ressource (vi, 149 Seiten) Illustrationen |
| ISBN: | 9783319213057 9783319213040 |
| DOI: | 10.1007/978-3-319-21305-7 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804175846709133312 |
|---|---|
| adam_text | LECTURES ON FUNCTOR HOMOLOGY
/
: 2015
TABLE OF CONTENTS / INHALTSVERZEICHNIS
INTRODUCTION
A. DJAMENT: HOMOLOGIE STABLE DES GROUPES A COEFFICIENTS POLYNOMIAUX
W. VAN DER KALLEN:LECTURES ON BIFUNCTORS ANDFINITE GENERATION OF
RATIONALCOHOMOLOGY ALGEBRAS
R. MIKHAILOV: POLYNOMIAL FUNCTORS AND HOMOTOPY THEORY
A. TOUZE: PREREQUISITES OF HOMOLOGICAL ALGEBRA
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
LECTURES ON FUNCTOR HOMOLOGY
/
: 2015
ABSTRACT / INHALTSTEXT
THIS BOOK FEATURES A SERIES OF LECTURES THAT EXPLORES THREE DIFFERENT
FIELDS IN WHICH FUNCTOR HOMOLOGY (SHORT FOR HOMOLOGICAL ALGEBRA IN
FUNCTOR CATEGORIES) HAS RECENTLY PLAYED A SIGNIFICANT ROLE. FOR EACH OF
THESE APPLICATIONS, THE FUNCTOR VIEWPOINT PROVIDES BOTH ESSENTIAL
INSIGHTS AND NEW METHODS FOR TACKLING DIFFICULT MATHEMATICAL PROBLEMS.
IN THE LECTURES BY AURELIEN DJAMENT, POLYNOMIAL FUNCTORS APPEAR AS
COEFFICIENTS IN THE HOMOLOGY OF INFINITE FAMILIES OF CLASSICAL GROUPS,
E.G. GENERAL LINEAR GROUPS OR SYMPLECTIC GROUPS, AND THEIR
STABILIZATION. DJAMENT’S THEOREM STATES THAT THIS STABLE HOMOLOGY CAN
BE COMPUTED USING ONLY THE HOMOLOGY WITH TRIVIAL COEFFICIENTS AND THE
MANAGEABLE FUNCTOR HOMOLOGY. THE SERIES INCLUDES AN INTRIGUING
DEVELOPMENT OF SCORICHENKO’S UNPUBLISHED RESULTS. THE LECTURES BY
WILBERD VAN DER KALLEN LEAD TO THE SOLUTION OF THE GENERAL COHOMOLOGICAL
FINITE GENERATION PROBLEM, EXTENDING HILBERT’S FOURTEENTH PROBLEM AND
ITS SOLUTION TO THE CONTEXT OF COHOMOLOGY. THE FOCUS HERE IS ON THE
COHOMOLOGY OF ALGEBRAIC GROUPS, OR RATIONAL COHOMOLOGY, AND THE
COEFFICIENTS ARE FRIEDLANDER AND SUSLIN’S STRICT POLYNOMIAL FUNCTORS,
A CONCEPTUAL FORM OF MODULES OVER THE SCHUR ALGEBRA. ROMAN MIKHAILOV’S
LECTURES HIGHLIGHT TOPOLOGICAL INVARIANTS: HOMOTOPY AND HOMOLOGY OF
TOPOLOGICAL SPACES, THROUGH DERIVED FUNCTORS OF POLYNOMIAL FUNCTORS. IN
THIS REGARD THE FUNCTOR FRAMEWORK MAKES BETTER USE OF NATURALITY,
ALLOWING IT TO REACH CALCULATIONS THAT REMAIN BEYOND THE GRASP OF
CLASSICAL ALGEBRAIC TOPOLOGY. LASTLY, ANTOINE TOUZE’S INTRODUCTORY
COURSE ON HOMOLOGICAL ALGEBRA MAKES THE BOOK ACCESSIBLE TO GRADUATE
STUDENTS NEW TO THE FIELD. THE LINKS BETWEEN FUNCTOR HOMOLOGY AND THE
THREE FIELDS MENTIONED ABOVE OFFER COMPELLING ARGUMENTS FOR PUSHING THE
DEVELOPMENT OF THE FUNCTOR VIEWPOINT. THE LECTURES IN THIS BOOK WILL
PROVIDE READERS WITH A FEEL FOR FUNCTORS, AND A VALUABLE NEW PERSPECTIVE
TO APPLY TO THEIR FAVOURITE PROBLEMS
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
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| author_facet | Franjou, Vincent 1959- Touzé, Antoine |
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| dewey-ones | 512 - Algebra |
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| discipline | Mathematik |
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| isbn | 9783319213057 9783319213040 |
| language | English French |
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| spelling | Lectures on functor homology Vincent Franjou, Antoine Touzé, editors Cham Birkhäuser [2015] Cham Springer 1 Online-Ressource (vi, 149 Seiten) Illustrationen txt rdacontent c rdamedia cr rdacarrier Progress in mathematics volume 311 Beiträge in englischer und französischer Sprache Mathematics Category theory (Mathematics) Homological algebra Group theory Algebraic topology Category Theory, Homological Algebra Group Theory and Generalizations Algebraic Topology Mathematik Franjou, Vincent 1959- (DE-588)114366357 edt Touzé, Antoine (DE-588)1081398353 edt Progress in mathematics volume 311 (DE-604)BV035421267 311 https://doi.org/10.1007/978-3-319-21305-7 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028730341&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028730341&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Lectures on functor homology Progress in mathematics Mathematics Category theory (Mathematics) Homological algebra Group theory Algebraic topology Category Theory, Homological Algebra Group Theory and Generalizations Algebraic Topology Mathematik |
| title | Lectures on functor homology |
| title_auth | Lectures on functor homology |
| title_exact_search | Lectures on functor homology |
| title_full | Lectures on functor homology Vincent Franjou, Antoine Touzé, editors |
| title_fullStr | Lectures on functor homology Vincent Franjou, Antoine Touzé, editors |
| title_full_unstemmed | Lectures on functor homology Vincent Franjou, Antoine Touzé, editors |
| title_short | Lectures on functor homology |
| title_sort | lectures on functor homology |
| topic | Mathematics Category theory (Mathematics) Homological algebra Group theory Algebraic topology Category Theory, Homological Algebra Group Theory and Generalizations Algebraic Topology Mathematik |
| topic_facet | Mathematics Category theory (Mathematics) Homological algebra Group theory Algebraic topology Category Theory, Homological Algebra Group Theory and Generalizations Algebraic Topology Mathematik |
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