Prym Representations and Twisted Cohomology of the Mapping Class Group with Level Structures

Xiyan Zhong

doi:10.2140/gt.2026.30.155

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arXiv · 2401.13869

Prym Representations and Twisted Cohomology of the Mapping Class Group with Level Structures

Xiyan Zhong

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Abstract

We compute the twisted cohomology of the mapping class group with level structures, with coefficients in the $r$-tensor powers of the Prym representations for any positive integer $r$. When $r\ge 2$, we show that the cohomology exhibits instability for large genus, whereas it remains stable for $r=0$ or $r=1$. As a corollary, we prove that the symplectic Prym representation associated with any finite abelian regular cover of a non-closed finite-type surface is infinitesimally rigid.

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BibTeX RIS

Xiyan Zhong. 2024-01-25. Prym Representations and Twisted Cohomology of the Mapping Class Group with Level Structures. https://doi.org/10.2140/gt.2026.30.155

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