Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 12, Number 1 (2012), 95-108.
On piecewise linear cell decompositions
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.
Algebr. Geom. Topol., Volume 12, Number 1 (2012), 95-108.
Received: 21 June 2011
Accepted: 17 October 2011
First available in Project Euclid: 19 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57Q15: Triangulating manifolds
Kirillov, Jr, Alexander. On piecewise linear cell decompositions. Algebr. Geom. Topol. 12 (2012), no. 1, 95--108. doi:10.2140/agt.2012.12.95. https://projecteuclid.org/euclid.agt/1513715333