**Seminario Teoría de grupos**

**Alan McLeay**

** (Glasgow)**

**"Ivanov’s Metaconjecture"**

**Miércoles 3 de mayo, sala 520, M-17**

**14:30 horas **

**Abstract: The extended mapping class group of a surface is the group whose elements are precisely the isotopy classes of all boundary preserving homeomorphisms of the surface. It is a well-known and fundamental result of Ivanov that the curve complex (or curve graph) of an orientable surface with punctures has automorphism group isomorphic to the extended mapping class group of the surface. It was subsequently shown that the equivalent statement is true for a number of other complexes, among them the pants complex (Margalit) and the separating curve complex (Brendle-Margalit, Kida). Such results led Ivanov to make a meta-conjecture: all sufficiently rich objects related to the surface will have automorphism group isomorphic to the extended mapping class group. A result by Brendle-Margalit shows this to be true for a broad class of complexes for closed surfaces. In this talk I will give the more general result for complexes relating to surfaces with punctures.**