2210.03720Oct 7, 202227 pages, 15 figures, 1 table. There are important changes from version 1, where Theorem 3.10 was false. The overall proof strategy remains the same; changes mirror those from v2 to v3 of arXiv.2008.06490. Also, the diagrammatic correspondence introduced in version 1 is now introduced instead in arXiv.2210.03225, as are "lassos."

The virtual flyping theorem

Thomas Kindred

Geometric Topology

arXiv PDF

Abstract

We extend the flyping theorem to alternating links in thickened surfaces and alternating virtual links. The proof of the former result uses work of Boden--Karimi to adapt the author's geometric proof of Tait's 1898 flyping conjecture (first proved in 1993 by Menasco--Thistlethwaite), while the proof of the latter involves a diagrammatic correspondence recently introduced by the author in a related paper. In the process, we also extend a classical result of Gordon--Litherland, establishing an isomorphism between their pairing on a spanning surface and the intersection form on a 4-manifold constructed as a double-branched cover using that surface.

Briefing

What this paper is actually doing

Sign in and connect a model key to generate a briefing for this paper.

Socratic margin

Ask the abstract

Questions are grounded in the title and abstract. If the PDF is required, arXivDesk will say so.

Sign in to ask questions about this paper.