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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Square complexes and simplicial nonpositive curvature


Authors: Tomasz Elsner and Piotr Przytycki
Journal: Proc. Amer. Math. Soc. 141 (2013), 2997-3004
MSC (2010): Primary 20F65
Published electronically: May 15, 2013
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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.


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Additional Information

Tomasz Elsner
Affiliation: Mathematical Institute, University of Wrocław, Plac Grunwaldzki 2/4, 50-384 Wrocław, Poland
Email: elsner@math.uni.wroc.pl

Piotr Przytycki
Affiliation: Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warsaw, Poland
Email: pprzytyc@mimuw.edu.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11568-6
PII: S 0002-9939(2013)11568-6
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
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.