## Topology & Geometric Group Theory Seminar

## Fall 2009

### 1:30 – 2:30, Malott 203

Tuesday, October 27

**Fred
Cohen**, University of Rochester

*Generalized moment-angle complexes*

A subspace of a product space known as 'the generalized moment-angle
complex' was first defined in generality by Neil Strickland extending
constructions of Davis-Januskiewicz, Buchstaber-Panov-Ray, and
Goresky-MacPherson.

Definitions, examples, as well as connections to other topics will be
addressed. One notable case is given by subspaces of products of
infinite dimensional complex projective space 'indexed by a finite
simplicial complex'.

These spaces encode features ranging from the structure of toric
varieties in one guise, Stanley-Reisner rings of simplicial complexes,
as well as 'motions of certain types of robotic legs' in other guises.

What do these spaces have to do with the motions of legs of a
cockroach? This feature will be illustrated with slides.

Features of these spaces such as their cohomology as well as stable
structure are developed within the context of classical homotopy
theory based on joint work with A. Bahri, M. Bendersky, and S. Gitler.
Applications to the motion of legs of a cockroach are based on joint
work with G. Haynes and D. Koditschek.

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