Doubly slice knots and L^2 signatures by Patrick Orson

Geometry Topology Seminar
Monday, April 15, 2019 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 006
Patrick Orson – Boston College – patrick.orson@bc.edu
JungHwan Park

The question of which high-dimensional knots are slice was entirely solved by Kervaire and Levine. Compared to this, the question of which knots are doubly slice in high-dimensions is still a largely open problem. Ruberman proved that in every dimension, some version of the Casson-Gordon invariants can be applied to obtain algebraically doubly slice knots that are not doubly slice. I will show how to use L^2 signatures to recover the result of Ruberman for (4k-3)-dimensional knots, and discuss how the derived series of the knot group might be used to organise the high-dimensional doubly slice problem.