Speaker:  Nikolay Erochovets (Moscow State University)

Date and time:  8.12.2021, 17:00 (GMT +03:00)

Title: Canonical geometrization of orientable 3-manifolds defined by vector-colourings of 3-polytopes

Abstract:  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.

To access the online seminar please contact  Anna Tolbey bekvaanna@gmail.com