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Geometriae Dedicata

, Volume 114, Issue 1, pp 147–188 | Cite as

Combinatorial Harmonic Maps and Discrete-group Actions on Hadamard Spaces

  • Hiroyasu Izeki
  • Shin Nayatani
Article

Abstract

In this paper we use the combinatorial harmonic map theory to study the isometric actions of discrete groups on Hadamard spaces. Given a finitely generated group acting by automorphisms, properly discontinuously and cofinitely on a simplicial complex and its isometric action on a Hadamard spaces, we formulate criterions for the action to have a global fixed point.

Keywords

building discrete group Hadamard space harmonic map simplicial complex superrigidity 

Mathematics Subject Classifications (2000)

58E20 22E40  51E24 

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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Mathematical InstituteTohoku UniversitySendaiJapan
  2. 2.Graduate School of MathematicsNagoya UniversityChikusa-kuJapan

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