Upsilon invariant for graphs and homology cobordism group of homology cylinders

Geometry Topology Seminar
Monday, April 11, 2022 - 2:00pm for 1 hour (actually 50 minutes)
skies 006
Akram Alishahi – UGA – Akram.Alishahi@uga.edu
Beibei Liu

Upsilon is an invariant of knots defined using knot Floer homology by Ozsváth, Szabó and Stipsicz. In this talk, we discuss a generalization of their invariant for embedded graphs in rational homology spheres satisfying specific properties. Our construction will use a generalization of Heegaard Floer homology for “generalized tangles” called tangle Floer homology. As a result, we get a family of homomorphisms from the homology cobordism group of homology cylinders (over a surface of genus 0), which is an enlargement of the mapping class group defined by Graoufaldis and Levine.