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Non-involutory Hopf algebras and 3-manifold invariants
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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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Integrals along bimonoid homomorphisms
For Hopf monoid homomorphisms, a normalized generator integral exists exactly when the kernel admits an integral and the cokernel admits a cointegral.
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