Date-Day-Time : 26th August, Tuesday, 4 pm

Host:  Sudarshan R. Gurjar

Venue: Ramanujan Hall

Speaker: Ankur Sarkar

Title- Smooth Structures on the product of a 4 manifold with a
standard sphere.

Abstract- The study of exotic smooth structures on manifolds is one of
the fundamental problems in topology. In particular, the
classification of smooth structures on a given smooth manifold M is
connected to the determination of a subgroup of the group of homotopy
spheres, namely, the concordance inertia group of M. In this talk, we
compute the concordance inertia group of the product of a 4 manifold M
with the standard k-sphere using the stable homotopy type of M, where
k varies between 1 to 10. Using the above computations of the
concordance inertia group, we classify all smooth manifolds
homeomorphic to the product of M with the standard k-spheres, up to
concordance. As an application of the above computations, we give a
complete diffeomorphism classification of closed, oriented, smooth
manifolds homeomorphic to the product of complex 2 projective space
with standard k-sphere, where k lies between 4 and 6. This is a joint
work with Samik Basu and Ramesh Kasilingam.