A rational cohomology which including that of a spin hyperelliptic mapping class group

2025/03/31 by Fu, Yan, Wang, Gefei
#14H30 #57K20 #FOS: Mathematics #Geometric Topology (math.GT) #Primary 20F36 #Secondary 20J06

paper · doi:10.48550/arxiv.2503.23787

Abstract

Let \mathfrakG=\mathfrakS_q \overleftrightarrow× \mathfrakS_q be the ℤ/2-extension of the product of two symmetric groups \mathfrakS_q × \mathfrakS_q. In this paper, we compute the \mathfrakG-invariant part of the rational cohomology of the pure braid group P_n. This includes the rational cohomology of a spin hyperelliptic mapping class group of genus g, where 2g+2=n=2q.

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