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- W2963273309 abstract "The Lodha–Moore groups provide the first known examples of type [Formula: see text] groups that are non-amenable and contain no non-abelian free subgroups. These groups are related to Thompson’s group [Formula: see text] in certain ways, for instance they contain it as a subgroup in a natural way. We exhibit decompositions of four Lodha–Moore groups, [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], into ascending HNN extensions of isomorphic copies of each other, both in ways reminiscent to such decompositions for [Formula: see text] and also in quite different ways. This allows us to prove two new topological results about the Lodha–Moore groups. First, we prove that they all have trivial homotopy groups at infinity; in particular they are the first examples of groups satisfying all four parts of Geoghegan’s 1979 conjecture about [Formula: see text]. Second, we compute the Bieri–Neumann–Strebel invariant [Formula: see text] for the Lodha–Moore groups, and get some partial results for the Bieri–Neumann–Strebel–Renz invariants [Formula: see text], including a full computation of [Formula: see text]." @default.
- W2963273309 created "2019-07-30" @default.
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- W2963273309 date "2016-09-08" @default.
- W2963273309 modified "2023-10-12" @default.
- W2963273309 title "HNN decompositions of the Lodha–Moore groups, and topological applications" @default.
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- W2963273309 doi "https://doi.org/10.1142/s1793525316500242" @default.
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