Skip to main content
Browse by:

Until further notice, in-person public events have been canceled. Event listings include how to access online content.
Please check before coming to campus.

Homology spheres, knots, and cobordisms

Duke Math
Icon calendar
Wednesday, February 26, 2020
Icon time
12:00 pm - 1:00 pm
Icon speaker
Linh Truong (Institute for Advanced Study, School of Mathematics)
Icon series
Geometry/topology Seminar

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.