Kirillov, Alexander jun. On piecewise linear cell decompositions. (English) Zbl 1283.57026 Algebr. Geom. Topol. 12, No. 1, 95-108 (2012). 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. Cited in 1 ReviewCited in 5 Documents MSC: 57Q15 Triangulating manifolds Keywords:cell decomposition; triangulating manifolds PDF BibTeX XML Cite \textit{A. Kirillov jun.}, Algebr. Geom. Topol. 12, No. 1, 95--108 (2012; Zbl 1283.57026) Full Text: DOI arXiv References: [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.