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Quasiautomorphism
groups of type $F_\infty$
Samuel Audino, Delaney R Aydel and Daniel S Farley |
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Algebraic & Geometric Topology 18 (2018) 2339–2369
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Abstract |
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The groups , , , and are groups of quasiautomorphisms of the infinite binary tree. Their names indicate a similarity with Thompson’s well-known groups , and . We will use the theory of diagram groups over semigroup presentations to prove that all of the above groups (and several generalizations) have type . 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 cubical complexes. |
Keywords
quasiautomorphism group, Thompson's groups, Houghton
groups, finiteness properties of groups, CAT(0) cubical
complexes
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Mathematical Subject Classification 2010
Primary: 20F65
Secondary: 57M07
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References |
Publication
Received: 3 May 2017
Revised: 27 October 2017
Accepted: 6 February 2018
Published: 26 April 2018
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Authors |
| Samuel Audino | |
| Brooklyn, NY United States |
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| Delaney R Aydel | |
| Department of Mathematics Miami University Oxford, OH United States |
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| Daniel S Farley | |
| Department of Mathematics Miami University Oxford, OH United States |
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