End-essential spanning surfaces for links in thickened surfaces

Thomas Kindred

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arXiv · 2210.03218

End-essential spanning surfaces for links in thickened surfaces

Thomas Kindred

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Abstract

Let $D$ be a cellular alternating link diagram on a closed orientable surface $Σ$. We prove that if $D$ has no removable nugatory crossings then each checkerboard surface from $D$ is $π_1$-essential and contains no essential closed curve that is $\partial$-parallel in $Σ\times I$. Our chief motivation comes from technical aspects of a companion paper, where we prove that Tait's flyping conjecture holds for alternating virtual links. We also describe possible applications via Turaev surfaces.

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BibTeX RIS

Thomas Kindred. 2024-08-29. End-essential spanning surfaces for links in thickened surfaces. https://arxiv.org/abs/2210.03218

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