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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
Audino, Samuel 1 ; Aydel, Delaney 2 ; Farley, Daniel 2
@article{10_2140_agt_2018_18_2339,
author = {Audino, Samuel and Aydel, Delaney and Farley, Daniel},
title = {Quasiautomorphism groups of type {F\ensuremath{\infty}}},
journal = {Algebraic and Geometric Topology},
pages = {2339--2369},
publisher = {mathdoc},
volume = {18},
number = {4},
year = {2018},
doi = {10.2140/agt.2018.18.2339},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.2339/}
}
TY - JOUR AU - Audino, Samuel AU - Aydel, Delaney AU - Farley, Daniel TI - Quasiautomorphism groups of type F∞ JO - Algebraic and Geometric Topology PY - 2018 SP - 2339 EP - 2369 VL - 18 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.2339/ DO - 10.2140/agt.2018.18.2339 ID - 10_2140_agt_2018_18_2339 ER -
%0 Journal Article %A Audino, Samuel %A Aydel, Delaney %A Farley, Daniel %T Quasiautomorphism groups of type F∞ %J Algebraic and Geometric Topology %D 2018 %P 2339-2369 %V 18 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.2339/ %R 10.2140/agt.2018.18.2339 %F 10_2140_agt_2018_18_2339
Audino, Samuel; Aydel, Delaney; Farley, Daniel. Quasiautomorphism groups of type F∞. Algebraic and Geometric Topology, Tome 18 (2018) no. 4, pp. 2339-2369. doi: 10.2140/agt.2018.18.2339
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