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.
"On piecewise linear cell decompositions." Algebr. Geom. Topol. 12 (1) 95 - 108, 2012. https://doi.org/10.2140/agt.2012.12.95