Volume 18, issue 4 (2018)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 5, 2509–3131
Issue 4, 1883–2507
Issue 3, 1259–1881
Issue 2, 635–1258
Issue 1, 1–633

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Quasiautomorphism groups of type $F_\infty$

Samuel Audino, Delaney R Aydel and Daniel S Farley

Algebraic & Geometric Topology 18 (2018) 2339–2369
Abstract

The groups QF, QT, Q̄T, Q̄V and QV are groups of quasiautomorphisms of the infinite binary tree. Their names indicate a similarity with Thompson’s well-known groups F, T and V .

We will use the theory of diagram groups over semigroup presentations to prove that all of the above groups (and several generalizations) have type F. Our proof uses certain types of hybrid diagrams, which have properties in common with both planar diagrams and braided diagrams. The diagram groups defined by hybrid diagrams also act properly and isometrically on CAT(0) cubical complexes.

Keywords
quasiautomorphism group, Thompson's groups, Houghton groups, finiteness properties of groups, CAT(0) cubical complexes
Mathematical Subject Classification 2010
Primary: 20F65
Secondary: 57M07
References
Publication
Received: 3 May 2017
Revised: 27 October 2017
Accepted: 6 February 2018
Published: 26 April 2018
Authors
Samuel Audino
Brooklyn, NY
United States
Delaney R Aydel
Department of Mathematics
Miami University
Oxford, OH
United States
Daniel S Farley
Department of Mathematics
Miami University
Oxford, OH
United States