Algebraic & Geometric Topology

On piecewise linear cell decompositions

Alexander Kirillov, Jr

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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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57Q15: Triangulating manifolds

cell decomposition 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.

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