NON-REALIZABILITY OF BRAID GROUPS BY DIFFEOMORPHISMS

2023-8-10
UĞURLU, NALAN SENA
The mapping class group is the group of isotopy classes of orientation preserving diffeomorphisms of a surface. The realization problem asks if a given subgroup lifts to the group of orientation preserving diffeomorphisms. Morita's non-lifting theorem gives a negative answer to the realization problem for infinite subgroups of the mapping class group. In this thesis, we focus on two different proofs of this theorem one due to Bestvina, Church and Souto, and the other due to Salter and Tshishiku. For this purpose, in the first proof, we will consider an arbitrary finite index subgroup of the mapping class group directly, and we will consider the result with different numbers of marked points as well. In the second proof, we will consider the braid group, then use this to prove Morita's result.
Citation Formats
N. S. UĞURLU, “NON-REALIZABILITY OF BRAID GROUPS BY DIFFEOMORPHISMS,” M.S. - Master of Science, Middle East Technical University, 2023.