Jan 22 2020

Special Colloquium: Homology spheres, knots, and cobordisms, by Linh Truong

January 22, 2020

3:00 PM - 3:50 PM


636 SEO


Chicago, IL

Linh Truong (Institute for Advanced Study): Homology spheres, knots, and cobordisms

Homology 3-spheres, i.e. 3-dimensional manifolds with the same homology groups as the standard 3-sphere, play a central role in topology. Their study was initiated by Poincare in 1904, who constructed the first nontrivial example of a homology 3-sphere, and conjectured that the standard sphere is the only simply connected example. A century later, Poincare's conjecture was finally resolved by Perelman, but we are still far from understanding the general classification of homology 3-spheres.

This classification problem can be packaged in terms of the homology cobordism group, which is an abelian group formed by the set of all homology 3-spheres modulo a cobordism relation. I will survey what is known about this group, as well as discuss a closely related group classifying knots in the 3-sphere, including recent results joint with Irving Dai, Jennifer Hom, and Matthew Stoffregen.

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Julius Ross

Date posted

Jan 24, 2020

Date updated

Jan 24, 2020


Linh Truong | (Institute for Advanced Study)