Advanced Studies in Pure Mathematics

A fixed-point property of finitely generated groups and an energy of equivariant maps

Hiroyasu Izeki

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Abstract

The purpose of this article is to present sufficient conditions for an isometric action of a finitely generated group to have a fixed point in terms of an energy of equivariant maps (Proposition 2.1 and Theorem 3.1), which turn out to be useful in proving that groups with fixed-point property form a large family in the set of finitely presented groups. Most of the results are included in [7] and [8].

Article information

Source
Probabilistic Approach to Geometry, M. Kotani, M. Hino and T. Kumagai, eds. (Tokyo: Mathematical Society of Japan, 2010), 171-188

Dates
Received: 24 January 2009
Revised: 4 March 2009
First available in Project Euclid: 24 November 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543086318

Digital Object Identifier
doi:10.2969/aspm/05710171

Mathematical Reviews number (MathSciNet)
MR2648259

Zentralblatt MATH identifier
1201.58014

Subjects
Primary: 58E20: Harmonic maps [See also 53C43], etc. 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]

Keywords
Fixed-point property finitely generated groups harmonic maps

Citation

Izeki, Hiroyasu. A fixed-point property of finitely generated groups and an energy of equivariant maps. Probabilistic Approach to Geometry, 171--188, Mathematical Society of Japan, Tokyo, Japan, 2010. doi:10.2969/aspm/05710171. https://projecteuclid.org/euclid.aspm/1543086318


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