Author | Cherix, Pierre-Alain. author |
---|---|
Title | Groups with the Haagerup Property [electronic resource] : Gromov's a-T-menability / by Pierre-Alain Cherix, Paul Jolissaint, Alain Valette, Michael Cowling, Pierre Julg |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2001 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8237-8 |
Descript | VII, 126 p. online resource |
1 Introduction -- 1.1 Basic definitions -- 1.2 Examples -- 1.3 What is the Haagerup property good for? -- 1.4 What this book is about -- 2 Dynamical Characterizations -- 2.1 Definitions and statements of results -- 2.2 Actions on measure spaces -- 2.3 Actions on factors -- 3 Simple Lie Groups of Rank One -- 3.1 The Busemann cocycle and theGromov scalar product -- 3.2 Construction of a quadratic form -- 3.3 Positivity -- 3.4 The link with complementary series -- 4 Classification of Lie Groups with the Haagerup Property -- 4.0 Introduction -- 4.1 Step one -- 4.2 Step two -- 5 The Radial Haagerup Property -- 5.0 Introduction -- 5.1 The geometry of harmonic NA groups -- 5.2 Harmonic analysis on H-type groups -- 5.3 Analysis on harmonic NA groups -- 5.4 Positive definite spherical functions -- 5.5 Appendix on special functions -- 6 Discrete Groups -- 6.1 Some hereditary results -- 6.2 Groups acting on trees -- 6.3 Group presentations -- 6.4 Appendix: Completely positive mapson amalgamated products,by Paul Jolissaint -- 7 Open Questions and Partial Results -- 7.1 Obstructions to the Haagerup property -- 7.2 Classes of groups -- 7.3 Group constructions -- 7.4 Geometric characterizations -- 7.5 Other dynamical characterizations