IMSA Distinguished Speaker Series
Dr. Ian Hambleton, McMaster University
Ungar, Room 528B
Wednesday, October 2, 2024, 5pm (the general public talk)
Title: Euler characteristics in dimension four
Abstract: The topology and total curvature of a Riemann surface is determined by a single integer, the Euler characteristic (Leonhard Euler, 1707-1783). While this is not the case in dimension four, the Euler characteristic still gives interesting invariants for finitely presented groups. For example, what is the minimum possible value for the Euler characteristic of a closed 4-manifold with a given fundamental group ? The talk will survey some recent joint work with Alejandro Adem on this theme.
Thursday, October 3, 2024, 5pm (the more specialized talk)
Title: Finite 2-complexes and 4-manifolds
Abstract: From a finite 2-complex X, one can construct a closed, smooth 4-manifold M(X), for example as the boundary of a thickened embedding in 5-dimensional Euclidean space. If X and Y have isomorphic fundamental groups, then J H C Whiehead (1939) proved that X and Y become stably homotopy equivalent after adjoining a suitable number of copies of the 2-sphere. The talk will discuss the analogous 4-dimensional stable and unstable uniqueness question. We produce arbitrarily large families of smooth 4-manifolds M(X), by varying X with a given fundamental group, which are all stably diffeomorphic but pairwise distinct up to homotopy. This is joint work in progress with John Nicholson (U Glasgow).
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