Abstract:Given a natural number k and an orientable surface S of finite type, define the k-curve graph to be the graph with vertices corresponding to isotopy classes of essential simple closed curves on S and with edges corresponding to pairs of such curves admitting representatives that intersect at most k times. We prove that the automorphism group of the k-curve graph of a surface S is isomorphic to the extended mapping class group for all k satisfying k ≤ |χ(S)| − 512. We prove the same result for the so-called sys… Show more
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