7 citations · 10 across the 2 of their papers we have counts for
6 papers · 1 filter
Detecting knot invertibility
Greg Kuperberg
We discuss the consequences of the possibility that Vassiliev invariants do not detect knot invertibility as well as the fact that quantum Lie group invariants are known not to do…
Non-involutory Hopf algebras and 3-manifold invariants
Greg Kuperberg
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.…
Web bases for sl(3) are not dual canonical
Mikhail Khovanov, Greg Kuperberg
We compare two natural bases for the invariant space of a tensor product of irreducible representations of A_2, or sl(3). One basis is the web basis, defined from a skein theory ca…
Quadrisecants of knots and links
Greg Kuperberg
We show that every non-trivial tame knot or link in R^3 has a quadrisecant, i.e. four collinear points. The quadrisecant must be topologically non-trivial in a precise sense. As an…
Another proof of the alternating sign matrix conjecture
Greg Kuperberg
Robbins conjectured, and Zeilberger recently proved, that there are 1!4!7!...(3n-2)!/n!/(n+1)!/.../(2n-1)! alternating sign matrices of order n. We give a new proof of this result…
Another homogeneous, non-bihomogeneous Peano continuum
Greg Kuperberg
K. Kuperberg found a locally connected, finite-dimensional continuum which is homogeneous but not bihomogeneous. We give a similar but simpler example. Like previous constructions,…