#### 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.

Notes on file formats
W B R Lickorish

Department of Pure Mathematics and Mathematical Statistics

University of Cambridge

16, Mill Lane, Cambridge, CB2 1SB, UK

Email: wbrl@dpmms.cam.ac.uk

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