Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.18261 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917029378785280 |
|---|---|
| author | Stavrou, Andreas |
| author_facet | Stavrou, Andreas |
| contents | Let $Σ_{g,*}$ be a once-punctured oriented surface of genus $g$. We study the action of the mapping class group $Γ_{g,*}$ on the $n^{th}$ rational cohomology of the configuration space $\text{Conf}_n(Σ_{g,*})$ of injections $\{1,\ldots, n\}\hookrightarrow Σ_{g,*}$, and compare the kernel $J_{g,*}^{cfg}(n)$ of this action with the $n^{th}$ Johnson subgroup $J_{g,*}(n)$. We find high-rank abelian subgroups in the quotient $J_{g,*}^{cfg}(n)/J_{g,*}(n)$ arising from the higher Johnson images and from symplectic representation theory. In particular we refute a conjecture due to Bianchi--Miller--Wilson. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_18261 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Surface configuration kernels Stavrou, Andreas Geometric Topology Let $Σ_{g,*}$ be a once-punctured oriented surface of genus $g$. We study the action of the mapping class group $Γ_{g,*}$ on the $n^{th}$ rational cohomology of the configuration space $\text{Conf}_n(Σ_{g,*})$ of injections $\{1,\ldots, n\}\hookrightarrow Σ_{g,*}$, and compare the kernel $J_{g,*}^{cfg}(n)$ of this action with the $n^{th}$ Johnson subgroup $J_{g,*}(n)$. We find high-rank abelian subgroups in the quotient $J_{g,*}^{cfg}(n)/J_{g,*}(n)$ arising from the higher Johnson images and from symplectic representation theory. In particular we refute a conjecture due to Bianchi--Miller--Wilson. |
| title | Surface configuration kernels |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2510.18261 |