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Comparing Invariants of 3-Manifolds Derived from Hopf Algebras
Sequin, Matthew James

2012, Doctor of Philosophy, Ohio State University, Mathematics.
This paper will compare two different quantum 3-manifold invariants, both of which are given using a finite dimensional Hopf Algebra H. One is the Hennings invariant, given by an algorithm involving the link surgery presentation of a 3-manifold and the Drinfeld double D(H); the other is the Kuperberg invariant, which is computed using a Heegaard diagram of the 3-manifold and the same H. We show that when H is semi-simple, these two invariants are equal. The proof is entirely in Hopf algebraic terms and does not rely on the representation theory of H or general results involving categorical invariants.
Thomas Kerler (Advisor)
Zbigniew Fiedorowicz (Committee Member)
Nathan Broaddus (Committee Member)
106 p.

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Sequin, M. (2012). Comparing Invariants of 3-Manifolds Derived from Hopf Algebras. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Sequin, Matthew. "Comparing Invariants of 3-Manifolds Derived from Hopf Algebras." Electronic Thesis or Dissertation. Ohio State University, 2012. OhioLINK Electronic Theses and Dissertations Center. 26 Sep 2017.

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Sequin, Matthew "Comparing Invariants of 3-Manifolds Derived from Hopf Algebras." Electronic Thesis or Dissertation. Ohio State University, 2012. https://etd.ohiolink.edu/

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