Geodesic
On piecewise linear cell decompositions
Kirillov, Jr, Alexander1
1Department of Mathematics, SUNY at Stony Brook, Stony Brook, NY 11794, USA
Algebraic and Geometric Topology, Tome 12 (2012) no. 1, pp. 95-108
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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.

DOI : 10.2140/agt.2012.12.95
Keywords: cell decomposition, Triangulating manifolds

Kirillov, Jr, Alexander  1

1 Department of Mathematics, SUNY at Stony Brook, Stony Brook, NY 11794, USA 
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Kirillov, Jr, Alexander. On piecewise linear cell decompositions. Algebraic and Geometric Topology, Tome 12 (2012) no. 1, pp. 95-108. doi: 10.2140/agt.2012.12.95

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[3] R Oeckl, Discrete gauge theory: From lattices to TQFT, Imperial College Press (2005)

[4] C P Rourke, B J Sanderson, Introduction to piecewise-linear topology, , Springer (1982)

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