# 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)

`tpanov@mech.math.msu.su`

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.

**References**
[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.