Chennai Mathematical Institute


3:30 pm, Seminar Hall
Cohen-Macaulay property for topological spaces

Priyavrat Deshpande
Chennai Mathematical Institute.


A characterization of Cohen-Macaulay rings states that the local cohomology of these rings vanishes in the middle dimensions. A similar phenomenon can be observed, as a consequence of Poincare duality, in the context of closed aspherical manifolds; their cohomology with local coefficients is concentrated only in the top dimension and is rank 1. In recent years a lot of authors have determined conditions under which cohomology with coefficients in a (rank 1) complex local system vanishes. In this talk I will describe a spectral sequence developed by Denham-Suciu-Yuzvinsky which helps determine some of these vanishing conditions. My focus will be on spaces that arise in the context of manifold reflection groups. This is ongoing work with Ronno Das