November 8, 2025

On the rational cohomology of spin hyperelliptic mapping class groups

Key Points

Independent rational cohomology dimensions identified in mapping class groups, reinforcing algebraic foundations.
Key metrics include dimension calculations across all degrees for hyperelliptic and braid groups.
Analysis of spin hyperelliptic mapping class groups within rational cohomology framework reveals structural insights.
Findings enhance understanding of invariant parts in algebraic topology relevant to pure braid group.

Abstract

Let Formula: see text be the subgroup Formula: see text of the Formula: see text-th symmetric group Formula: see text for Formula: see text. In this paper, we study the Formula: see text-invariant part of the rational cohomology group of the pure braid group Formula: see text. The invariant part includes the rational cohomology of a spin hyperelliptic mapping class group of genus Formula: see text as a subalgebra when Formula: see text, denoted by Formula: see text. Based on the study of Lehrer-Solomon 8, we prove that they are independent of Formula: see text and Formula: see text in degree Formula: see text. We also give a formula to calculate the dimension of Formula: see text and calculate it in all degrees for Formula: see text.

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Cite This Study

Gefei Wang (Fri,) studied this question.

synapsesocial.com/papers/690e8b6ca5b062d7a4e735ab https://doi.org/https://doi.org/10.1142/s1793525326500044

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