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A note on the homology of hyperbolic groups

A note on the homology of hyperbolic groups Hyperbolic groups have been studied in various fields in mathematics. They appear in contexts as diverse as geometric group theory, function theory (as Fuchsian groups) and algebraic topology (as fundamental groups of compact hyperbolic surfaces). Hyperbolic groups possess geometrical properties well suited for the study of homological finiteness conditions. In this paper we will prove some of these results via free resolutions obtained from the Rips-complex. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Groups - Complexity - Cryptology de Gruyter

A note on the homology of hyperbolic groups

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Publisher
de Gruyter
Copyright
© de Gruyter 2010
ISSN
1867-1144
eISSN
1869-6104
DOI
10.1515/GCC.2010.012
Publisher site
See Article on Publisher Site

Abstract

Hyperbolic groups have been studied in various fields in mathematics. They appear in contexts as diverse as geometric group theory, function theory (as Fuchsian groups) and algebraic topology (as fundamental groups of compact hyperbolic surfaces). Hyperbolic groups possess geometrical properties well suited for the study of homological finiteness conditions. In this paper we will prove some of these results via free resolutions obtained from the Rips-complex.

Journal

Groups - Complexity - Cryptologyde Gruyter

Published: Dec 1, 2010

Keywords: Hyperbolic groups; Rips-complex; homology of groups; Fuchsian groups

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