Princeton-Rider Workshop on Homotopy Theory and Toric Spaces (sponsored by Algebraic Topology Seminar)

2/23/2012

Alex Suciu
Northeastern University

 

Polyhedral products, toric manifolds, and twisted cohomology

 

I will discuss the cohomology with coefficients in rank one local systems for various polyhedral products, including real Davis-Januszkiewicz spaces and toric complexes. As one application (joint work with Alvise Trevisan), I will show how to determine the Betti numbers and the cup products of real, quasi-toric manifolds. As another application (joint work with Graham Denham and Sergey Yuzvinsky), I will explain why Cohen-Macaulay toric complexes enjoy a certain "abelian duality" property.