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- Title
Virtual Seifert surfaces.
- Authors
Chrisman, Micah
- Abstract
A virtual knot that has a homologically trivial representative 𝒦 in a thickened surface Σ × [ 0 , 1 ] is said to be an almost classical (AC) knot. 𝒦 then bounds a Seifert surface F ⊂ Σ × [ 0 , 1 ]. Seifert surfaces of AC knots are useful for computing concordance invariants and slice obstructions. However, Seifert surfaces in Σ × [ 0 , 1 ] are difficult to construct. Here, we introduce virtual Seifert surfaces of AC knots. These are planar figures representing F ⊂ Σ × [ 0 , 1 ]. 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.
- Subjects
KNOT theory; POLYNOMIALS; CHARTS, diagrams, etc.; ALGORITHMS; CONCORDANCES (Topology)
- Publication
Journal of Knot Theory & Its Ramifications, 2019, Vol 28, Issue 6, pN.PAG
- ISSN
0218-2165
- Publication type
Article
- DOI
10.1142/S0218216519500391