Square complexes and simplicial nonpositive curvature
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- by Tomasz Elsner and Piotr Przytycki PDF
- Proc. Amer. Math. Soc. 141 (2013), 2997-3004 Request permission
Abstract:
We prove that each nonpositively curved square $\mathcal {VH}$-complex can be turned functorially into a locally $6$-large simplicial complex of the same homotopy type. It follows that any group acting properly and cocompactly on a CAT(0) square $\mathcal {VH}$-complex is systolic. In particular, the product of two finitely generated free groups is systolic, which answers a question of Daniel Wise. On the other hand, we exhibit an example of a non-$\mathcal {VH}$ nonpositively curved square complex whose fundamental group is neither systolic nor even virtually systolic.References
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Additional Information
- Tomasz Elsner
- Affiliation: Mathematical Institute, University of Wrocław, Plac Grunwaldzki 2/4, 50-384 Wrocław, Poland
- MR Author ID: 858149
- Email: elsner@math.uni.wroc.pl
- Piotr Przytycki
- Affiliation: Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warsaw, Poland
- MR Author ID: 804559
- Email: pprzytyc@mimuw.edu.pl
- Received by editor(s): July 20, 2011
- Received by editor(s) in revised form: November 21, 2011
- Published electronically: May 15, 2013
- Additional Notes: The first author was partially supported by MNiSW grant N N201 541 738
The second author was partially supported by MNiSW grant N N201 541 738 and the Foundation for Polish Science - Communicated by: Alexander N. Dranishnikov
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 2997-3004
- MSC (2010): Primary 20F65
- DOI: https://doi.org/10.1090/S0002-9939-2013-11568-6
- MathSciNet review: 3068952