Research Seminars @ Illinois

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Tailored for undergraduate researchers, this calendar is a curated list of research seminars at the University of Illinois. Explore the diverse world of research and expand your knowledge through engaging sessions designed to inspire and enlighten.

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GGT seminar: Exotic Aspherical 4-manifolds

Event Type: Seminar/Symposium
Sponsor: Groups, Geometry, and Topology Seminar
Location: 347 Altgeld Hall
Date: Apr 10, 2025 11:00 am - 12:00 pm
Speaker: Nathan Sunukjian (Calvin College)
Views: 82
Originating Calendar: Groups, Geometry, and Topology Calendar; Abstract: Examples of exotic 4-manifolds, which are homeomorphic but not diffeomorphic, are plentiful, but not well understood. Most examples are constructed via modification: some kind of surgery is done on an embedded surface where, one hopes and prays that the topological structure is preserved, but some smooth invariant is changed. This talk will discuss examples of exotic 4-manifolds that are aspherical, and the peculiarities involved in constructing them and detecting that they are exotic. These 4-manifolds provide a counterexample to the smooth Borel conjecture in dimension 4, which states that a homotopy equivalence between 4-manifolds should be homotopic to a diffeomorphism. This is joint work with Mike Davis, Kyle Hayden, Jingyin Huang, and Danny Ruberman.

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