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Invariants of 4-manifolds from Hopf algebras

[Moved Online] Tensor categories and topological quantum field theories March 16, 2020 - March 20, 2020

March 16, 2020 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Xingshan Cui (Purdue University)
  • invariants

  • 4-manifolds

  • Hopf algebras

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The Kuperberg invariant is a quantum invariant of 3-manifolds based on any finite dimensional Hopf algebras, which is also related to the Turaev-Viro-Barrett-Westbury invariant. We give a construction of an invariant of 4-manifolds that can be viewed as a 4-dimensional analog of the Kuperberg invariant. The algebraic data for the construction is what we call a Hopf triple which consists of three Hopf algebras and a bilinear form on each pair of the Hopf algebras satisfying certain compatibility conditions. Quasi-triangular Hopf algebras are special examples of Hopf triples. Trisection diagrams of 4-manifolds proposed by Gay and Kirby will be used in the construction of the invariant. Some interesting properties of the invariant will also be discussed.

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