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On piecewise linear cell decompositions

Alexander Kirillov, Jr
Algebraic & Geometric Topology 12 (2012) 95–108
DOI: 10.2140/agt.2012.12.95
Abstract

We introduce a class of cell decompositions of PL manifolds and polyhedra which are more general than triangulations yet not as general as CW complexes; we propose calling them PLCW complexes. The main result is an analog of Alexander’s theorem: any two PLCW decompositions of the same polyhedron can be obtained from each other by a sequence of certain “elementary” moves.

This definition is motivated by the needs of Topological Quantum Field Theory, especially extended theories as defined by Lurie.

Keywords
cell decomposition, Triangulating manifolds
Mathematical Subject Classification 2000
Primary: 57Q15
References
Publication
Received: 21 June 2011
Accepted: 17 October 2011
Published: 15 February 2012
Authors
Alexander Kirillov, Jr
Department of Mathematics
SUNY at Stony Brook
Stony Brook, NY 11794
USA
http://www.math.sunysb.edu/~kirillov/