Volume 18, issue 4 (2018)

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Quasiautomorphism groups of type $F_\infty$

Samuel Audino, Delaney R Aydel and Daniel S Farley

Algebraic & Geometric Topology 18 (2018) 2339–2369

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.

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quasiautomorphism group, Thompson's groups, Houghton groups, finiteness properties of groups, CAT(0) cubical complexes
Mathematical Subject Classification 2010
Primary: 20F65
Secondary: 57M07
Received: 3 May 2017
Revised: 27 October 2017
Accepted: 6 February 2018
Published: 26 April 2018
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