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Abstract: Asymptotic mapping class groups was introduced by Funar and Kapoudjian. They can be treated as a generalization of the Thompson groups in the mapping class group setting. We will discuss how these groups are constructed and show that they are in fact of type F_infinity. The proof boils down to prove certain subsurface complexes are highly connected. This is based on joint work with Javier Aramayona, Kai-Uwe Bux, Jonas Flechsig and Nansen Petrosyan.