### Branched cyclic covers and L-spaces

- Series
- Geometry Topology Seminar
- Time
- Wednesday, July 7, 2021 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Hannah Turner – University of Texas, Austin

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.