Combinatorial Harmonic Maps and Discrete-group Actions on Hadamard Spaces

被引：0
作者：
Hiroyasu Izeki
Shin Nayatani
机构：
[1] Tohoku University,Mathematical Institute
[2] Nagoya University,Graduate School of Mathematics
来源：
Geometriae Dedicata | 2005年 / 114卷
关键词：
building; discrete group; Hadamard space; harmonic map; simplicial complex; superrigidity; 58E20; 22E40; 51E24;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
引用
收藏
页码：147 / 188
页数：41
相关论文
共 35 条
[1]  
Ballmann W.(1997)On Geom. Funct. Anal. 7 615-645
[2]  
Światkowski J.(1988)-cohomology and property (T) for automorphism groups of polyhedral cell complexes J. Differential Geom. 28 361-382
[3]  
Corlette K.(1992)Flat G-bundles with canonical metrics Ann. Math. 135 165-182
[4]  
Corlette K.(1987)Archimedian superrigidity and hyperbolic geometry Proc. London Math. Soc. 55 127-131
[5]  
Donaldson S. K.(1964)Twisted harmonic maps and the self-duality equations Amer. J. Math. 86 109-160
[6]  
Eells J.(1964)Harmonic maps of Riemannian manifolds J. Algebra 1 114-131
[7]  
Sampson J. H.(1973)The nonexistence of certain generalized polygons Ann. Math. 97 375-423
[8]  
Feit W.(2003)-adic curvature and the cohomology of discrete subgroups of Geom. Funct. Anal. 13 73-148
[9]  
Higman G.(1992)-adic groups Publ. Math. IHES 76 165-246
[10]  
Garland H.(2003)Random walk in random groups Perspectives of Hyperbolic Spaces (Kyoto, 2002), RIMS Kokyuroku 1329 1-7
1234