SMS scnews item created by Catherine Meister at Mon 16 Jun 2025 1505
Type: Seminar
Distribution: World
Expiry: 30 Jun 2025
Calendar1: 19 Jun 2025 1300-1400
CalLoc1: SMRI Seminar Room (Macleay Building A12 Room 301)
CalTitle1: SMRI Seminar: From surfaces to 4-manifolds: a leisurely journey in the topology of manifolds
Auth: cmeister@10.48.21.53 (cmei0631) in SMS-SAML

SMRI Seminar

From surfaces to 4-manifolds: a leisurely journey in the topology of manifolds

Crowley

From surfaces to 4-manifolds: a leisurely journey in the topology of manifolds

Speaker: Diarmuid Crowley, University of Melbourne

Abstract: Let F be a closed connected orientable surface (2-manifold). Here are two foundational facts in the study of surfaces:

1) F_1 and F_2 are homeomorphic if and only if they have the same Euler characteristic;

2) Every self-homotopy equivalence of F is homotopic to a homeomorphism.

In this talk will I review these facts and then move to dimension 4, where the analogous statements for 4-manifolds are far from true. Indeed, in finding weak analogues of (1), i.e. necessary and sufficient conditions for two 4-manifolds within some class to be homeomorphic, it is often helpful to have counter-examples to the strict analogue of (2); i.e. self-homotopy equivalences of 4-manifolds which are not homotopic to homeomorphisms. The last part of this talk will contain a preliminary report on new examples of such 'exotic self-homotopy equivalences', which have shown up in joint work with Daniel Kasprowski, Mark Powell, and Arunima Ray.

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