Links all of whose branched covers are L-spaces

Hannah Turner (UT Austin)

Abstract: Given an oriented link in the three-sphere and a fixed positive integer n, there is a unique 3-manifold called its branched cyclic cover of index n. It is not well understood when these manifolds are L-spaces - that is, when their Heegaard Floer homology is as simple as possible. In this talk I'll describe a new construction of links whose cyclic branched covers are L-spaces for any index n. The proof uses a symmetry argument and a generalization of alternating links due to Scaduto-Stoffregen. This is joint work with Ahmad Issa.