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A nonamenable type F ∞ group of piecewise projective homeomorphisms
Author(s) -
Lodha Yash
Publication year - 2020
Publication title -
journal of topology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.447
H-Index - 31
eISSN - 1753-8424
pISSN - 1753-8416
DOI - 10.1112/topo.12172
Subject(s) - mathematics , type (biology) , group (periodic table) , element (criminal law) , pure mathematics , piecewise , projective test , projective representation , combinatorics , algebra over a field , mathematical analysis , ecology , chemistry , organic chemistry , political science , law , biology
We prove that the group of homeomorphisms of the circle introduced by the author with Justin Moore is of type F ∞ . This makes the group the first example of a type F ∞ group which is nonamenable and does not contain nonabelian free subgroups. To prove our result, we provide a certain generalisation of cube complexes, which we refer to as cluster complexes . We also obtain a computable normal form , or a canonical unique choice of a word for each element of the group.