Equivariant surgery formulas in Heegaard Floer theory

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Kristen Hendricks, Rutgers University
Fine Hall 314

A core computational feature of Ozsváth and Szabó's Heegaard Floer theory is its possession of a surgery formula; that is, given a knot K in S^3, the Heegaard Floer three-manifold invariants of Dehn surgery on K can be computed from the knot Floer homology of K, and similarly (albeit more complicatedly) for surgeries on links. In this talk we prove an equivariant version of the Heegaard Floer knot surgery formula for symmetric knots in S^3; that is, given a symmetry on a knot, we compute the induced action on the surgery complex. The proof goes by way of showing naturality of certain bimodules constructed by Zemke to encode the data of the link surgery formula. As an application, we show that the kernel of the forgetful map from the equivariant homology cobordism group to the homology cobordism group contains a Z^infty summand. This is joint work with A. Mallick, M. Stoffregen, and I. Zemke.