Tuesday, October 27
Fred Cohen, University of Rochester
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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