Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 20J05, 20F65

Retrieve articles in all journals with MSC (2000): 20J05, 20F65


Additional Information

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

DOI: https://doi.org/10.1090/S0002-9947-04-03720-1
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.