NON-REALIZABILITY OF BRAID GROUPS BY DIFFEOMORPHISMS

Date

2023-8-10

Author

UĞURLU, NALAN SENA

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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.

Subject Keywords

Mapping Class Groups, Braid Groups, Orientation Preserving Diffeomorphisms, Morita’s Non-lifting Theorem

URI

https://hdl.handle.net/11511/104886

Collections

Graduate School of Natural and Applied Sciences, Thesis