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Automorphisms of the K-curve Graph by Agrawal, Shuchi; Aougab, Tarik; Chandran, Yassin; Loving, Marissa; Oakley, J. Robert; Shapiro, Roberta; Xiao, Yang is a scholarly article available to read on EtoBox.

What is Automorphisms of the K-curve Graph about?

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 sufficiently small with respect to the Euler characteristic of S. We prove the same result for the so-called systolic complex, a variant of the curve graph whose complete subgraphs encode the intersection patterns for any collection of systoles with respect to a hyperbolic metric. This resolves a conjecture of Schmutz Schaller.

Author

Agrawal, Shuchi; Aougab, Tarik; Chandran, Yassin; Loving, Marissa; Oakley, J. Robert; Shapiro, Roberta; Xiao, Yang

Published

2019

Language

EN