Topology + Geometry
32nd Summer Conference on Topology and Its Applications
Here we introduce the notion of virtual Seifert surfaces. Virtual Seifert surfaces may be thought of as a generalization of Gauss diagrams of virtual knots to spanning surfaces of a knot. This device is then employed to extend the Tristram-Levine signature function to AC knots. Using the AC signature functions and Tuarev’s graded genus invariant, we determine the slice status of all 76 almost classical knots having at most six crossings. The slice obstructions for AC knots are then extended to all virtual knots via the parity projection map. This map, which is computable from a Gauss diagram, sends a concordance class of virtual knots to a concordance class of AC knots.
Copyright © 2017, the Authors
Chrisman, Micah; Boden, Hans U.; and Gaudreau, Robin, "Virtual Seifert Surfaces and Slice Obstructions For Knots in Thickened Surfaces" (2017). Summer Conference on Topology and Its Applications. 42.