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Moduli spaces of local systems and higher Teichmüller theory:

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Bibliographic Details
Main Authors:	Fock, V. V. (Author), Goncharov, A. B. (Author)
Format:	Book
Language:	English
Published:	Bonn Max-Planck-Inst. 2004
Series:	MPI 2004,76
Online Access:	Inhaltsverzeichnis
Physical Description:	114 S. graph. Darst.

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adam_text	MODULI SPACES OF LOCAL SYSTEMS AND HIGHER TEICHMULLER THEORY V. V. FOCK A. B. GONCHAROV SUB GOTTINGEN 7 218 169 68X K2005B5035 MAX-PLANCK-LNSTITUT FUR MATHEMATIK VIVATSGASSE 7 53111 BONN GERMANY BROWN UNIVERSITY MPI 04-76 MODULI SPACES OF LOCAL SYSTEMS AND HIGHER TEICHMULLER THEORY V.V. FOCK, A. B. GONCHAXOV CONTENTS 1 INTRODUCTION 1 2 THE MODULI SPACES A G § AND X Q § 12 3 SURFACES, GRAPHS, MAPPING CLASS GROUPS AND GROUPOIDS 19 4 ELEMENTS OF POSITIVE ALGEBRAIC GEOMETRY 23 5 POSITIVE CONFIGURATIONS OF FLAGS 27 6 A POSITIVE STRUCTURE ON THE MODULI SPACE X G § 38 7 A POSITIVE STRUCTURE ON THE MODULI SPACE A G § 51 8 SPECIAL COORDINATES ON THE A AND X SPACES WHEN G IS OF TYPE A M 60 9 THE PAIR (X PGL §,A SL §) CORRESPONDS TO AN ORBI-CLUSTER ENSEMBLE 76 10 THE CLASSICAL TEICHMULLER SPACES 84 11 LAMINATIONS AND CANONICAL PAIRINGS 86 12 POSITIVE COORDINATE SYSTEMS FOR ^-LAMINATIONS 100 13 A WEIL-PETERSSON FORM ON A G § AND ITS MOTIVIC AVATAR 103 1 INTRODUCTION 1 AN ALGEBRAIC-GEOMETRIC APPROACH TO HIGHER TEICHMULLER THEORY. LET S BE A SURFACE WITH N HOLES. THE TEICHMULLER SPACE TS IS THE MODULI SPACE OF COMPLEX STRUCTURES ON S MODULO DIFFEO- MORPHISMS ISOTOPIC TO THE IDENTITY. WE WILL USUALLY ASSUME THAT S IS HYPERBOLIC, I.E. X( THEN THE POINCARE UNIFORMISATION THEOREM IDENTIFIES IT WITH THE SPACE OF ALL FAITHFUL REPRESENTATIONS TTI(S) - PSL,2(R) FITH DISCRETE IMAGE, MODULO CONJUGATIONS BY PSL,2(M.)- TRADITIONALLY THE TE- ICHMULLER THEORY IS CONSIDERED AS A PART OF ANALYSIS AND GEOMETRY. THE TEICHMULLER SPACE IS BY NO MEANS A SET OF REAL POINTS OF AN ALGEBRAIC VARIETY. INDEED, DIS- CRETENESS IS NOT A CONDITION OF AN ALGEBRAIC NATURE. IN THIS PAPER WE SHOW THAT, NEVERTHELESS, THERE IS AN ALGEBRAIC-GEOMETRIC APPROACH TO THE TEICHMULLER THEORY. MOREOVER WE SHOW THAT IT ADMITS A GENERALIZATION WHERE PSL2 IS REPLACED BY A SPLIT SEMI-SIMPLE ALGEBRAIC GROUP G WITH TRIVIAL CENTER. HERE ARE THE MAIN FEATURES OF OUR STORY. V .
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id	DE-604.BV025346685
illustrated	Illustrated
indexdate	2024-07-09T22:31:35Z
institution	BVB
language	English
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physical	114 S. graph. Darst.
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spelling	Fock, V. V. Verfasser aut Moduli spaces of local systems and higher Teichmüller theory V. V. Fock ; A. B. Goncharov Bonn Max-Planck-Inst. 2004 114 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier MPI 2004,76 Goncharov, A. B. Verfasser aut Max-Planck-Institut <Bonn> MPI 2004,76 (DE-604)BV035932118 2004,76 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019974547&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Fock, V. V. Goncharov, A. B. Moduli spaces of local systems and higher Teichmüller theory
title	Moduli spaces of local systems and higher Teichmüller theory
title_auth	Moduli spaces of local systems and higher Teichmüller theory
title_exact_search	Moduli spaces of local systems and higher Teichmüller theory
title_full	Moduli spaces of local systems and higher Teichmüller theory V. V. Fock ; A. B. Goncharov
title_fullStr	Moduli spaces of local systems and higher Teichmüller theory V. V. Fock ; A. B. Goncharov
title_full_unstemmed	Moduli spaces of local systems and higher Teichmüller theory V. V. Fock ; A. B. Goncharov
title_short	Moduli spaces of local systems and higher Teichmüller theory
title_sort	moduli spaces of local systems and higher teichmuller theory
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019974547&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV035932118
work_keys_str_mv	AT fockvv modulispacesoflocalsystemsandhigherteichmullertheory AT goncharovab modulispacesoflocalsystemsandhigherteichmullertheory

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