Geometry/Topology Seminar

Monday, October 18, 2021 at 3:00pm to 4:00pm

Building 2, 2-449
182 MEMORIAL DR, Cambridge, MA 02139

Featured Speaker: Robert Burklund (MIT)

Title: A classification of metastable manifolds.

A basic goal in differential topology is to classify all smooth, closed, oriented n-manifolds up to diffeomorphism. As stated, this goal is too ambitious. However, for large n and with strong restrictions on the topology of the manifold progress becomes possible. In this talk, I will begin by discussing the classification of simply-connected manifolds whose only nonzero homology groups are H_0, H_{n/2}, and H_n, from the seminal work of Wall to its final resolution by the speaker and his collaborators. Then, I will discuss the extension of this classification into the metastable range, where the condition on the homology groups is relaxed so that H_0, H_{n/3 + e}, ..., H_{2n/3 -e} and H_n may be nonzero ( e is an error term growing sublinearly in n ). These manifolds are distinguished by the feature that the ring structure on their cohomology groups is entirely recorded by Poincare duality. Time permitting, I'll indicate how modern homotopy-theoretic methods can exploit metastability. This talk represents joint works with Andy Senger and Jeremy Hahn.

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