Geometry of the space of triangulations of a compact manifold (Q1925001)

The set of triangulations of a compact manifold \(M\), (of dimension \(\geq 4)\) may be given a metric by making the distance between triangulations the minimum number of ``bistellar operations'' (shellings) required to transform one to the other. The author proves a number of results which decisively, effectively and quantitatively demonstrate the undecidability results of Novikov on unrecognizabilty of manifold equivalences. The existence of a large number of remotely scattered triangulations with bounded number of simplices is also proved.