Geometry & Topology Monographs 2 (1999), Proceedings of the Kirbyfest, paper no. 16, pages 299-320.

Simplicial moves on complexes and manifolds

W B R Lickorish

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.

Keywords. Simplicial complexes, subdivisions, stellar subdivisions, stellar manifolds, Pachner moves

AMS subject classification. Primary: 57Q15. Secondary: 52B70.

E-print: arXiv:math.GT/9911256

Submitted: 7 December 1998. (Revised: 23 May 1999.) Published: 20 November 1999.

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W B R Lickorish
Department of Pure Mathematics and Mathematical Statistics
University of Cambridge
16, Mill Lane, Cambridge, CB2 1SB, UK

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