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.
