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

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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.

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Authors and Affiliations

  1. Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH, 43210-1174, USA

    Raeyong Kim

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  1. Raeyong Kim
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Correspondence to Raeyong Kim.

Additional information

This paper is a part of the author’s Ph.D. thesis. The author would like to thank thesis advisor Ian Leary for his guidance throughout this research project. The author also would like to thank Jean Lafont for his careful reading of an earlier version of this paper.

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Kim, R. Every finite complex has the homology of some \({\mathrm{CAT}(0)}\) cubical duality group. Geom Dedicata 176, 1–9 (2015). https://doi.org/10.1007/s10711-014-9956-4

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  • DOI: https://doi.org/10.1007/s10711-014-9956-4

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