Type: Article

First integral cohomology group of the pure mapping class group of a non-orientable surface of infinite type

Hernández Hernández, Jesús; Hidber, Cristhian E.;

Abstract:

In this work we compute the first integral cohomology of the pure mapping class group of a non-orientable surface of infinite topological type and genus at least 3. To this purpose, we also prove several other results already known for orientable surfaces such as the existence of an Alexan- der method, the fact that the mapping class group is isomorphic to the au- tomorphism group of the curve graph along with the topological rigidity of the curve graph, and the structure of the pure mapping class group as both a Polish group and a semi-direct product