Giovanni Framba (University of Pisa): Equivariant grid homology for strongly invertible knots

Abstract: 
A strongly invertible knot is a pair (K,\rho), where K \subset S^3 is a knot and \rho \in Diffeo^+(S^3) is an involution such that \rho(K) = K and \rho reverses the orientation on K. We show that, given a strongly invertible knot, it is always possible to present it through a symmetric grid G. Any two such symmetric grids for (K,\rho) are related by certain symmetric grid moves. In this talk, we induce an involution on the grid complex GC^-(G)$, and we use this additional structure to define an equivariant version of grid homology.

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