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Simplicial moves on complexes and manifolds

W B R Lickorish

Geometry & Topology Monographs 2 (1999) 299–320

DOI: 10.2140/gtm.1999.2.299

arXiv: math.GT/9911256

Abstract

Here are versions of the proofs of two classic theorems of combinatorial topology. The first is the result that piecewise linearly homeomorphic simplicial complexes are related by stellar moves. This is used in the proof, modelled on that of Pachner, of the second theorem. This states that moves from only a finite collection are needed to relate two triangulations of a piecewise linear manifold.

For Rob Kirby, a sixtieth birthday offering after thirty years of friendship.

Keywords

simplicial complexes, subdivisions, stellar subdivisions, stellar manifolds, Pachner moves

Mathematical Subject Classification

Primary: 57Q15

Secondary: 52B70

References
Publication

Received: 7 December 1998
Revised: 23 May 1999
Published: 20 November 1999

Authors
W B R Lickorish
Department of Pure Mathematics and Mathematical Statistics
University of Cambridge
16 Mill Lane
Cambridge
CB2 1SB
United Kingdom