Involutory Hopf algebras and 3-manifold invariants
Skip to main content
eScholarship
Open Access Publications from the University of California

Involutory Hopf algebras and 3-manifold invariants

  • Author(s): Kuperberg, Greg
  • et al.

Published Web Location

https://arxiv.org/pdf/math/9201301.pdf
No data is associated with this publication.
Abstract

We establish a 3-manifold invariant for each finite-dimensional, involutory Hopf algebra. If the Hopf algebra is the group algebra of a group $G$, the invariant counts homomorphisms from the fundamental group of the manifold to $G$. The invariant can be viewed as a state model on a Heegaard diagram or a triangulation of the manifold. The computation of the invariant involves tensor products and contractions of the structure tensors of the algebra. We show that every formal expression involving these tensors corresponds to a unique 3-manifold modulo a well-understood equivalence. This raises the possibility of an algorithm which can determine whether two given 3-manifolds are homeomorphic.

Item not freely available? Link broken?
Report a problem accessing this item