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Geometriae Dedicata

, Volume 176, Issue 1, pp 1–9 | Cite as

Every finite complex has the homology of some \({\mathrm{CAT}(0)}\) cubical duality group

  • Raeyong Kim
Original Paper
  • 101 Downloads

Abstract

We prove that every finite connected simplicial complex has the homology of the classifying space for some \({\mathrm{CAT}(0)}\) cubical duality group. More specifically, for any finite simplicial complex \(X\), we construct a locally \({\mathrm{CAT}(0)}\) cubical complex \(T_{X}\) and an acyclic map \(t_{X} : T_{X} \rightarrow X\) such that \(\pi _{1}(T_{X})\) is a duality group.

Keywords

The Kan–Thurston theorem Duality groups \(\mathrm{CAT}(0)\) cubical complexes 

Mathematics Subject Classification (2010)

55P20 20F67 (57P10, 20J05) 

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of MathematicsThe Ohio State UniversityColumbusUSA

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