Invariants of flat connections on 4-manifolds from Hopf group-algebras

Tomoro Mochida

doi:10.1142/s0218216526500136

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arXiv · 2402.17484

Invariants of flat connections on 4-manifolds from Hopf group-algebras

Tomoro Mochida

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Abstract

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.

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Tomoro Mochida. 2024-02-27. Invariants of flat connections on 4-manifolds from Hopf group-algebras. https://doi.org/10.1142/s0218216526500136

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