Algebraic & Geometric Topology

On piecewise linear cell decompositions

Alexander Kirillov, Jr

Full-text: Open access

Abstract

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.

Article information

Source
Algebr. Geom. Topol., Volume 12, Number 1 (2012), 95-108.

Dates
Received: 21 June 2011
Accepted: 17 October 2011
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715333

Digital Object Identifier
doi:10.2140/agt.2012.12.95

Mathematical Reviews number (MathSciNet)
MR2889547

Zentralblatt MATH identifier
1283.57026

Subjects
Primary: 57Q15: Triangulating manifolds

Keywords
cell decomposition Triangulating manifolds

Citation

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


Export citation

References

  • B Balsam, J Kirillov, Alexander, Turaev–Viro invariants as an extended TQFT
  • R Oeckl, Renormalization of discrete models without background, Nuclear Phys. B 657 (2003) 107–138
  • R Oeckl, Discrete gauge theory: From lattices to TQFT, Imperial College Press, London (2005)
  • C P Rourke, B J Sanderson, Introduction to piecewise-linear topology, Springer Study Edition, Springer, Berlin (1982)