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New Invariants of Homology Cobordism

  • Thursday, February 21, 2019
  • 3:40 PM–3:40 PM
  • North Hall 276

Kristen Hendricks, Michigan State University

This is a talk about 3-manifolds and knots. We will begin by reviewing some basic constructions and motivations in low-dimensional topology, and will then introduce the homology cobordism group, the group of 3-manifolds with the same homology as the 3-dimensional sphere up to a reasonable notion of equivalence. We will discuss what is known about the structure of this group and its connection to higher dimensional topology. We will then discuss some existing invariants of the homology cobordism group coming from gauge theory and symplectic geometry, particularly Floer theory. Finally, we will construct a new invariant of homology cobordism coming from an equivariant version of the computationally-friendly Floer-theoretic 3-manifold invariant Heegaard Floer homology, and use it to derive some structural applications. Parts of this talk are joint work with C. Manolescu and I. Zemke; more recent parts of this talk are joint work with J. Hom and T. Lidman.

Refreshments precede the talk at 3:30 p.m. in NH 276.

February 2019
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