Non-homogeneous combinatorial manifolds

Details Non-homogeneous combinatorial manifolds Non-homogeneous combinatorial manifolds

2011-08-24

arxiv.org/abs/1108.4955v1

Mathematics

Geometric Topology

18 pages, 6 figures

Scientific paper

In this paper we extend the classical theory of combinatorial manifolds to the non-homogeneous setting. NH-manifolds are polyhedra which are locally like Euclidean spaces of varying dimensions. We show that many of the properties of classical manifolds remain valid in this wider context. NH-manifolds appear naturally when studying Pachner moves on (classical) manifolds. We introduce the notion of NH-factorization and prove that PL-homeomorphic manifolds are related by a finite sequence of NH-factorizations involving NH-manifolds.

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