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arXiv · 1009.4227

On piecewise linear cell decompositions

Alexander Kirillov Jr
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Abstract

In this note, 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.

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Alexander Kirillov Jr. 2011-11-07. On piecewise linear cell decompositions. https://doi.org/10.2140/agt.2012.12.95

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