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

Primary: 57Q15

References

Publication

Received: 21 June 2011
Accepted: 17 October 2011
Published: 15 February 2012

Authors