Lefschetz Duality Revisited

Suppose M is a closed manifold and P\subset M is a polyhedron. Classical Lefschetz duality can be used to describe H^*(M\setminus P), the cohomology of the complement M\setminus P, as a graded module. However H^*(M\setminus P) also has an algebra structure and this structure can be determined whenever the dimension of P is small enough when compared to that of M. The methods developed to prove this are applied to describe the rational homotopy type of the blowup construction from algebraic geometry. This description of the rational homotopy type can be used to construct examples of symplectic non-Kahlerian manifolds.

Refreshments will be served at 2:45 p.m. in the Faculty Lounge, Math Annex (Room 1115).