Volume 14, issue 2 (2014)

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Aspherical manifolds that cannot be triangulated

Michael W Davis, Jim Fowler and Jean-François Lafont

Algebraic & Geometric Topology 14 (2014) 795–803
Abstract

By a result of Manolescu [arXiv:1303.2354v2] there are topological closed n–manifolds that cannot be triangulated for each n 5. We show here that for n 6 we can choose such manifolds to be aspherical.

Keywords
aspherical manifold, PL manifold, homology sphere, homology manifold, hyperbolization, triangulation, Rokhlin invariant
Mathematical Subject Classification 2010
Primary: 57Q15
Secondary: 20F65, 57Q25, 57R58
References
Publication
Received: 12 May 2013
Revised: 25 August 2013
Accepted: 6 September 2013
Published: 30 January 2014
Authors
Michael W Davis
Department of Mathematics
The Ohio State University
231 West 18th Ave.
Columbus, OH 43210-1174
USA
http://www.math.osu.edu/~davis.12/
Jim Fowler
Department of Mathematics
The Ohio State University
231 West 18th Ave.
Columbus, OH 43210-1174
USA
http://www.math.osu.edu/~fowler.291/
Jean-François Lafont
Department of Mathematics
The Ohio State University
231 West 18th Ave.
Columbus, OH 43210-1174
USA
http://www.math.osu.edu/~lafont.1/