Multiplicative dimensional reduction
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915644461547520 |
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| author | Kinjo, Tasuki |
| author_facet | Kinjo, Tasuki |
| contents | We prove the multiplicative version of the dimensional reduction theorem in cohomological Donaldson--Thomas theory. More precisely, we show that the BPS cohomology associated with the loop stack of a $0$-shifted symplectic stack admits a description analogous to orbifold cohomology, even though our stacks are not necessarily Deligne--Mumford. As an application, we propose a new, purely two-dimensional formulation of the topological mirror symmetry conjecture for the moduli space of $G$-Higgs bundles, which in turn leads to a formulation of the conjecture for logarithmic $G$-Higgs bundles. We also investigate a twisted version of the multiplicative dimensional reduction, which applies, in particular, to the cohomological Donaldson--Thomas theory for $S^1$-bundles over compact oriented surfaces, and more generally to Seifert-fibred $3$-manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_16342 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiplicative dimensional reduction Kinjo, Tasuki Algebraic Geometry Geometric Topology We prove the multiplicative version of the dimensional reduction theorem in cohomological Donaldson--Thomas theory. More precisely, we show that the BPS cohomology associated with the loop stack of a $0$-shifted symplectic stack admits a description analogous to orbifold cohomology, even though our stacks are not necessarily Deligne--Mumford. As an application, we propose a new, purely two-dimensional formulation of the topological mirror symmetry conjecture for the moduli space of $G$-Higgs bundles, which in turn leads to a formulation of the conjecture for logarithmic $G$-Higgs bundles. We also investigate a twisted version of the multiplicative dimensional reduction, which applies, in particular, to the cohomological Donaldson--Thomas theory for $S^1$-bundles over compact oriented surfaces, and more generally to Seifert-fibred $3$-manifolds. |
| title | Multiplicative dimensional reduction |
| topic | Algebraic Geometry Geometric Topology |
| url | https://arxiv.org/abs/2511.16342 |