Verfügbarkeit: A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their asymptotic geometry

A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their asymptotic geometry:

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Bibliographische Detailangaben
Beteilige Person:	Leeb, Bernhard (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Bonn Rheinische Friedrich-Wilhelms-Universität 2000
Schriftenreihe:	Bonner mathematische Schriften 326
Schlagwörter:	Hadamard-Mannigfaltigkeit Hochschulschrift
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009482874&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	42 S.

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adam_text	Titel: A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their a Autor: Leeb, Bernhard Jahr: 2000 A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their asymptotic geometry Bernhard Leeb* June 17, 1997 Abstract. We study geodesically complete and locally compact Hadamard spaces X whose Tits boundary is a connected irreducible spherical building. We show that X is symmetric iff complete geodesies in X do not branch and a Euclidean building otherwise. Furthermore, every boundary equivalence (cone topology homeomorphism preserving the Tits metric) between two such spaces is induced by a homothety. As an application, we can extend the Mostow and Prasad rigidity theorems to com- pact singular (orbi)spaces of nonpositive curvature which are homotopy equivalent to a quotient of a symmetric space or Euclidean building by a cocompact group of isometries. Contents 1 Introduction 2 1.1 Main result, background, motivation and an application................2 1-2 Around the argument......................................................5 2 Preliminaries 8 2.1 Hadamard spaces..........................................................8 2.1.1 Filling spheres at infinity by flats................................9 2.1.2 Convex cores ......................................................9 2.1.3 Spaces of strong asymptote classes . . 2.1.4 Types of isometries........... 2.2 Visibility Hadamard spaces........... 2.3 Buildings: Definition, vocabulary and examples 2.3.1 Spherical buildings........... 2.3.2 Euclidean buildings........... 2.4 Locally compact topological groups...... 3 Holonomy *Ieeb@math.uni-bonn.de 4 Rank one: Rigidity of highly symmetric visibility spaces 20 4.1 General properties . . . . . -....................21 4.2 Butterfly construction of small axial isometries . . . -..............22 4.3 The discrete case........................................................22 4.3.1 Equivariant rigidity for trees......................................25 4.4 The non-discrete case......................................................25 5 Geodesically complete Hadamard spaces with building boundary 27 5.1 Basic properties of parallel sets ...............................27 5.2 Boundary isomorphisms........... ......................28 5.3 The case of no branching.............. ............29 5.4 The case of branching ...... . . ....................34 5.4.1 Disconnectivity of Fiirstenberg boundary , ..............34 5.4.2 The structure of parallel sets . . ............36 5.4.3 Proof of the main result 1.2 . ..............37 5.5 Inducing boundary isomorphisms by homotheties: Proof of 1.3 .... 39 5.6 Extension of Mostow and Prasad Rigidity to singular spaces of non- positive curvature: Proofofl.5........................................40
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series	Bonner mathematische Schriften
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spellingShingle	Leeb, Bernhard A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their asymptotic geometry Bonner mathematische Schriften Hadamard-Mannigfaltigkeit (DE-588)4300462-3 gnd
subject_GND	(DE-588)4300462-3 (DE-588)4113937-9
title	A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their asymptotic geometry
title_auth	A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their asymptotic geometry
title_exact_search	A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their asymptotic geometry
title_full	A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their asymptotic geometry Bernhard Leeb
title_fullStr	A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their asymptotic geometry Bernhard Leeb
title_full_unstemmed	A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their asymptotic geometry Bernhard Leeb
title_short	A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their asymptotic geometry
title_sort	a characterization of irreducible symmetric spaces and euclidean buildings of higher rank by their asymptotic geometry
topic	Hadamard-Mannigfaltigkeit (DE-588)4300462-3 gnd
topic_facet	Hadamard-Mannigfaltigkeit Hochschulschrift
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009482874&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000001610
work_keys_str_mv	AT leebbernhard acharacterizationofirreduciblesymmetricspacesandeuclideanbuildingsofhigherrankbytheirasymptoticgeometry

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