Cohomological Donaldson-Thomas theory for local systems on the $3$-torus
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912042956357632 |
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| author | Kaubrys, Sarunas |
| author_facet | Kaubrys, Sarunas |
| contents | This paper studies the Cohomological Donaldson-Thomas theory of $G$-local systems on the topological three torus. Using an exponential map we prove cohomological integrality for $\mathrm{GL}_n$-local systems using the statement of cohomological integrality for the tripled Jordan quiver from Davison-Meinhardt (2020). Using this result we prove a version of cohomological integrality for $\mathrm{SL}_n$ and $\mathrm{PGL}_n$ for prime $n$. Finally, for prime $n$, we prove a Langlands duality statement for the $\mathrm{SL}_n$ and $\mathrm{PGL}_n$ cohomological Donaldson-Thomas invariants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16013 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cohomological Donaldson-Thomas theory for local systems on the $3$-torus Kaubrys, Sarunas Algebraic Geometry Geometric Topology Representation Theory This paper studies the Cohomological Donaldson-Thomas theory of $G$-local systems on the topological three torus. Using an exponential map we prove cohomological integrality for $\mathrm{GL}_n$-local systems using the statement of cohomological integrality for the tripled Jordan quiver from Davison-Meinhardt (2020). Using this result we prove a version of cohomological integrality for $\mathrm{SL}_n$ and $\mathrm{PGL}_n$ for prime $n$. Finally, for prime $n$, we prove a Langlands duality statement for the $\mathrm{SL}_n$ and $\mathrm{PGL}_n$ cohomological Donaldson-Thomas invariants. |
| title | Cohomological Donaldson-Thomas theory for local systems on the $3$-torus |
| topic | Algebraic Geometry Geometric Topology Representation Theory |
| url | https://arxiv.org/abs/2409.16013 |