Homological and finiteness properties of picture groups

Farley, Daniel

doi:10.1090/S0002-9947-04-03720-1

Homological and finiteness properties of picture groups
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by Daniel S. Farley PDF

Trans. Amer. Math. Soc. 357 (2005), 3567-3584 Request permission

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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