Equivariant Mapping Class Group and Orbit Braid Group*

Citation:

Shuya CAI,Hao LI.Equivariant Mapping Class Group and Orbit Braid Group*[J].Chinese Annals of Mathematics B,2022,43(4):485~498
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Authors:

Shuya CAI; Hao LI

Foundation:

National Natural Science Foundation of China (No. 11971112).
Abstract: Motivated by the work of Birman about the relationship between mapping class groups and braid groups, the authors discuss the relationship between the orbit braid group and the equivariant mapping class group on the closed surface M with a free and proper group action in this paper. Their construction is based on the exact sequence given by the fibration F0GM → F(M/G, n). The conclusion is closely connected with the braid group of the quotient space. Comparing with the situation without the group action, there is a big difference when the quotient space is T2.

Keywords:

Equivariant mapping class group, Orbit braid group, Evaluation map,Center of braid group

Classification:

20F36, 20F38, 37A20
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