Stably diffeomorphic manifolds and extended surgery
Diarmuid Crowley (University of Melbourne)
Monday 22nd July, 2024 16:00-17:00 Maths 311B
Abstract
The stable classes of a compact smooth 2q-manifold M is defined to be the set of diffeomorphism classes of manifolds which become diffeomorphic to M after connected sum with some number of copies of S^q x S^q, and which have the same Euler characteristic as M.
In recent joint work with Conway, Powell and Sixt, we used the algebra of modified surgery and extended symmetric forms to investigate the stable class, proving that in many cases it contains a large number of, or even infinitely many, homotopy types.
In parallel developments, Nagy has used extended symmetric forms to define extended versions of Kreck’s l-monoids and modified surgery obstruction. In this talk I will give an overview of the above developments. This talk samples aspects of joint work with Conway, Powell and Sixt and Nagy.
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