Branched cyclic covers and L-spaces

Geometry Topology Seminar
Wednesday, July 7, 2021 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 006
Hannah Turner – University of Texas, Austin
John Etnyre

A 3-manifold is called an L-space if its Heegaard Floer homology is "simple." No characterization of all such "simple" 3-manifolds is known. Manifolds obtained as the double-branched cover of alternating knots in the 3-sphere give examples of L-spaces. In this talk, I'll discuss the search for L-spaces among higher index branched cyclic covers of knots. In particular, I'll give new examples of knots whose branched cyclic covers are L-spaces for every index n. I will also discuss an application to "visibility" of certain periodic symmetries of a knot. Some of this work is joint with Ahmad Issa.