Invariants of flat connections on 4-manifolds from Hopf group-algebras
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866918311993802752 |
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| author | Mochida, Tomoro |
| author_facet | Mochida, Tomoro |
| contents | For a given group $G$, we construct an invariant of flat $G$-connections on 4-manifolds from a finite type involutory quasitriangular Hopf $G$-algebra. Hopf $G$-algebras are generalizations of Hopf algebras, equipped with gradings by $G$. In our construction, we color the dotted components of a Kirby diagram with elements of $G$ and employ the Hennings-type procedure. When $G$ is finite, we also define an invariant of 4-manifolds by summing the invariants over all flat $G$-connections. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17484 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Invariants of flat connections on 4-manifolds from Hopf group-algebras Mochida, Tomoro Geometric Topology Quantum Algebra For a given group $G$, we construct an invariant of flat $G$-connections on 4-manifolds from a finite type involutory quasitriangular Hopf $G$-algebra. Hopf $G$-algebras are generalizations of Hopf algebras, equipped with gradings by $G$. In our construction, we color the dotted components of a Kirby diagram with elements of $G$ and employ the Hennings-type procedure. When $G$ is finite, we also define an invariant of 4-manifolds by summing the invariants over all flat $G$-connections. |
| title | Invariants of flat connections on 4-manifolds from Hopf group-algebras |
| topic | Geometric Topology Quantum Algebra |
| url | https://arxiv.org/abs/2402.17484 |