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Virtual Seifert Surfaces
by
Micah Chrisman
Monmouth University
A virtual Seifert surface is a planar representation of a Seifert surface of a homologically trivial knot in a thickened surface Σ×[0, 1], where Σ is compact and oriented. The boundary of a virtual Seifert surface is a virtual knot. We present an algorithm for constructing them from a Gauss diagram of the virtual knot and show how they can be manipulated in the plane in a manner that is analogous to classical Seifert surfaces. Some applications are given. Firstly, virtual Seifert surfaces can be applied to the compute slice obstructions of virtual knots, such as directed signatures of almost classical knots. Secondly, the virtual Seifert surface algorithm gives rise to the notion of virtual canonical 3-genus of almost classical knots. This is compared to related notions in the literature, such as the slice genus, the virtual 3-genus, and the canonical genus of Stoimenow-Tchernov-Vdovina.
Date received: April 2, 2018
Copyright © 2018 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cboy-14.