On piecewise linear cell decompositions. (English) Zbl 1283.57026

Summary: 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.


57Q15 Triangulating manifolds
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[1] B Balsam, J Kirillov Alexander, Turaev-Viro invariants as an extended TQFT
[2] R Oeckl, Renormalization of discrete models without background, Nuclear Phys. B 657 (2003) 107 · Zbl 1023.81505
[3] R Oeckl, Discrete gauge theory: From lattices to TQFT, Imperial College Press (2005) · Zbl 1159.81006
[4] C P Rourke, B J Sanderson, Introduction to piecewise-linear topology, Springer Study Edition, Springer (1982) · Zbl 0477.57003
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