https://neckpinch.com/authors/nikolai-erokhovets/New arXiv papers by Nikolai Erokhovets, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2011.11628/arxiv:2011.11628Mon, 23 Nov 2020 00:00:00 GMTNikolai Erokhovets — In short geometrization conjecture of W.\,Thurston (finally proved by G. Perelman) says that any oriented 3-manifold can be canonically partitioned into pieces, which have a geometric structure of one of the eight types. In the seminal paper (1991) M.\,W.\,Davis and T.\,Januszkiewicz introduced a wide class of n-dimensional manifolds – small covers over simple n-polytopes. We give a complete answer to the following problem: to build an explicit canonical decomposition for any orientable 3-manifold defined by a vector-colouring of a simple 3-polytope, in particular for a small cover. The proof is based on analysis of results in this direction obtained before by different authors.Geometrization