Non-involutory Hopf algebras and 3-manifold invariants

Greg Kuperberg

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arXiv · q-alg/9712047

Non-involutory Hopf algebras and 3-manifold invariants

Greg Kuperberg

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Abstract

We present a definition of an invariant #(M,H), defined for every finite-dimensional Hopf algebra (or Hopf superalgebra or Hopf object) H and for every closed, framed 3-manifold M. When H is a quantized universal enveloping algebra, #(M,H) is closely related to well-known quantum link invariants such as the HOMFLY polynomial, but it is not a topological quantum field theory.

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Greg Kuperberg. 1997-12-19. Non-involutory Hopf algebras and 3-manifold invariants. https://arxiv.org/abs/q-alg/9712047

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