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ISSN 1088-6850(e) ISSN 0002-9947(p)

Homological and finiteness properties of picture groups

Author(s): Daniel S. Farley
Journal: Trans. Amer. Math. Soc. 357 (2005), 3567-3584.
MSC (2000): Primary 20J05, 20F65
Posted: 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 , , and .

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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