Geometry/topology Seminar

Monday, November 7, 2022, 3:15pm, Physics 119
Miriam Kuzbary (Georgia Tech, Mathematics)
Asymptotic bounds on the d-invariant

Abstract:

As shown by Morita, every integral homology 3-sphere Y has a Heegaard decomposition into two handlebodies where the gluing map along the boundary is an element of the Torelli subgroup of the mapping class group of the boundary composed with the standard gluing map for the 3-sphere. In work in progress with Santana Afton and Tye Lidman, we show that the d-invariant of Y, a homology cobordism invariant of homology spheres defined using Heegaard Floer homology, is bounded above by a linear function of the word length of a corresponding gluing element in the Torelli group for any fixed, finite generating set when the genus is larger than 2. Moreover, we show the d-invariant is bounded for homology spheres corresponding to various large families of mapping classes.

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