Manchester Geometry Seminar 2008/2009

Thursday 13 November 2008. The Frank Adams Room (Room 1.212), the Alan Turing Building. 4pm

Cohomological Rigidity in Toric Topology

Taras Panov (Moscow State University)

A family of closed manifolds is cohomologically rigid if the manifolds in the family are distinguished up to homeomorphism by their cohomology rings. Generally being a rare phenomenon, cohomological rigidity may be established for some families of manifolds arising in toric topology (Bott towers, toric and quasitoric manifolds, and moment-angle manifolds). There is also a related combinatorial concept of cohomological rigidity for simple polytopes: a polytope P is cohomologically rigid if its combinatorial type is determined by the integral cohomology ring of any (quasi)toric manifold over P.

We shall discuss several results on cohomological rigidity of toric families and certain polytopes, and suggest some open problems.

[1] Suyoung Choi, Mikiya Masuda and Dong Youp Suh. Quasi-toric manifolds over a product of simplices. Preprint, 2008; arXiv:0803.2749.
[2] Mikiya Masuda and Taras Panov. Semifree circle actions, Bott towers, and quasitoric manifolds. Sbornik Math., 199:6, 2008; arXiv:math.AT/0607094.