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Morse matchings on polytopes

R M Green and Jacob T Harper
Algebraic & Geometric Topology 12 (2012) 2429–2450
DOI: 10.2140/agt.2012.12.2429
Abstract

We show how to construct homology bases for certain CW complexes in terms of discrete Morse theory and cellular homology. We apply this technique to study certain subcomplexes of the half cube polytope studied in previous works. This involves constructing explicit complete acyclic Morse matchings on the face lattice of the half cube; this procedure may be of independent interest for other highly symmetric polytopes.

Keywords
discrete Morse theory, homology basis, half cube
Mathematical Subject Classification 2010
Primary: 52B11
References
Publication
Received: 25 July 2011
Revised: 28 May 2012
Accepted: 12 June 2012
Published: 25 January 2013
Authors
R M Green
Department of Mathematics
University of Colorado Boulder
Campus Box 395
Boulder CO 80309-0395
USA
http://math.colorado.edu/~rmg/
Jacob T Harper
Department of Mathematics
University of Colorado Boulder
Campus Box 395
Boulder CO 80309-0395
USA