Affiliation:
1. Department of Mathematics, The Ohio State University, Marion, OH 43302, USA
Abstract
A virtual knot that has a homologically trivial representative [Formula: see text] in a thickened surface [Formula: see text] is said to be an almost classical (AC) knot. [Formula: see text] then bounds a Seifert surface [Formula: see text]. Seifert surfaces of AC knots are useful for computing concordance invariants and slice obstructions. However, Seifert surfaces in [Formula: see text] are difficult to construct. Here, we introduce virtual Seifert surfaces of AC knots. These are planar figures representing [Formula: see text]. An algorithm for constructing a virtual Seifert surface from a Gauss diagram is given. This is applied to computing signatures and Alexander polynomials of AC knots. A canonical genus of AC knots is also studied. It is shown to be distinct from the virtual canonical genus of Stoimenow–Tchernov–Vdovina.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Cited by
3 articles.
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1. Algebraic concordance order of almost classical knots;Journal of Knot Theory and Its Ramifications;2023-10-15
2. The Gordon–Litherland pairing for links in thickened surfaces;International Journal of Mathematics;2022-09-15
3. Signature and concordance of virtual knots;Indiana University Mathematics Journal;2020