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End-essential spanning surfaces for links in thickened surfaces (2210.03218v2)
Published 6 Oct 2022 in math.GT
Abstract: Let $D$ be a cellular alternating link diagram on a closed orientable surface $\Sigma$. We prove that if $D$ has no removable nugatory crossings then each checkerboard surface from $D$ is $\pi_1$-essential and contains no essential closed curve that is $\partial$-parallel in $\Sigma\times I$. 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.