A metric Kan–Thurston theorem

By I. Leary. 2010

62 citations recorded by the source corpus.

For every simplicial complex X, we construct a locally CAT(0) cubical complex TX, a cellular isometric involution τ on TX and a map tX:TX→X with the following properties: tXτ=tX; tX is a homology isomorphism; the induced map from the quotient space TX/〈τ〉 to X is a homotopy equivalence; the induced map from the fixed point space TXτ to X is a homology isomorphism. The construction is functorial in X.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/26056a8ce3237a22bb86a6a130836f01a57308f7

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In Computational Theory and Mathematics

1. G. Hruska
2. Mark F. Hagen
3. Daniel T. Wise
4. Ilya Kapovich
5. Alexei G. Myasnikov

In Geometry and Topology

1. Mark F. Hagen
2. G. Hruska
3. Daniel T. Wise
4. Alessandro Sisto
5. Jason A. Behrstock
6. Frédéric Haglund
7. Anthony Genevois
8. Denis V. Osin

In Mathematical Physics

1. Mark F. Hagen
2. G. Hruska
3. Daniel T. Wise
4. Alessandro Sisto
5. Jason A. Behrstock
6. Anthony Genevois
7. Frédéric Haglund
8. Denis V. Osin

Citations in the corpus

• Finiteness properties of cubulated groups (2012, methodology): “This fact was verified by Moussong and Gromov in the finite dimensional case [Mou88, Gro87] and by Leary in the general case [Lea13].”
• Weak hyperbolicity of cube complexes and quasi‐arboreal groups (2011, result): “This also follows from more general results of Bridson, in the finite-dimensional case [5], and was extended by Leary to infinite-dimensional cube complexes [26].”