Polynomial bounds for surfaces in alternating link complements in 3-manifolds
Jessica S. PurcellAnastasiia Tsvietkova
Jessica S. PurcellAnastasiia Tsvietkova
Nov 2023
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摘要原文
There are recent polynomial bounds on the number of essential closed surfaces and spanning surfaces embedded in classical alternating link complements in terms of crossing number of the link diagram. Here, we give a more general result: polynomial bounds for links that have an alternating diagram on a closed surface in a compact irreducible 3-manifold. These are called weakly generalized alternating links, and include many links that are not classically alternating or do not lie in the 3-sphere. For example these include many virtual links and toroidally alternating links. Our bounds are for surfaces with arbitrary numbers of boundary components and arbitrary slopes. This gives the first polynomial bounds for surfaces with non-trivial slopes, or with multiple non-meridianal boundary components, even in the setting of classical alternating links.
