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- W3131748879 abstract "We prove a strengthened sector lemma for irreducible, finite-dimensional, locally finite, essential, cocompact CAT(0) cube complexes under the additional hypothesis that the complex is emph{hyperplane-essential}; we prove that every quarterspace contains a halfspace. In aid of this, we present simplified proofs of known results about loxodromic isometries of the contact graph, avoiding the use of disc diagrams. This paper has an expository element; in particular, we collect results about cube complexes proved by combining Ramsey's theorem and Dilworth's theorem. We illustrate the use of these tricks with a discussion of the Tits alternative for cubical groups, and ask some questions about ``quantifying'' statements related to rank-rigidity and the Tits alternative." @default.
- W3131748879 created "2021-03-01" @default.
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- W3131748879 date "2021-02-11" @default.
- W3131748879 modified "2023-09-25" @default.
- W3131748879 title "Large facing tuples and a strengthened sector lemma" @default.
- W3131748879 hasPublicationYear "2021" @default.
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