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Homological and finiteness properties of picture groups

Author: Daniel S. Farley
Journal: Trans. Amer. Math. Soc. 357 (2005), 3567-3584
MSC (2000): Primary 20J05, 20F65
Published electronically: December 9, 2004
MathSciNet review: 2146639
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Abstract: Picture groups are a class of groups introduced by Guba and Sapir. Known examples include Thompson's groups $F$, $T$, and $V$.

In this paper, a large class of picture groups is proved to be of type $F_{\infty}$. A Morse-theoretic argument shows that, for a given picture group, the rational homology vanishes in almost all dimensions.

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Additional Information

Daniel S. Farley
Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801

Keywords: Picture groups, diagram groups, finiteness properties of groups, Morse theory
Received by editor(s): December 4, 2003
Published electronically: December 9, 2004
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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