8 citations · 10 across the 3 of their papers we have counts for
6 papers
Novikov homology, jump loci and Massey products
Toshitake Kohno, Andrei Pajitnov
Let X be a finite CW-complex, denote its fundamental group by G. Let R be an n-dimensional complex repesentation of G. Any element A of the first cohomology group of X with complex…
Free subgroups within the images of quantum representations
Louis Funar, Toshitake Kohno
We prove that, except for a few explicit roots of unity, the quantum image of any Johnson subgroup of the mapping class group contains an explicit free non-abelian subgroup.
Circle-valued Morse theory for complex hyperplane arrangements
Toshitake Kohno, Andrei Pajitnov
Let A be an essential complex hyperplane arrangement in an n-dimensional complex vector space V. Let H denote the union of the hyperplanes, and M denote the complement to H in V. W…
On Burau representations at roots of unity
Louis Funar, Toshitake Kohno
We consider subgroups of the braid groups which are generated by -th powers of the standard generators and prove that any infinite intersection (with even ) is trivial. This…
Problems on invariants of knots and 3-manifolds
J. E. Andersen, N. Askitas, D. Bar-Natan +57
This is a list of open problems on invariants of knots and 3-manifolds with expositions of their history, background, significance, or importance. This list was made by editing ope…
Loop spaces of configuration spaces and finite type invariants
Toshitake Kohno
The total homology of the loop space of the configuration space of ordered distinct n points in R^m has a structure of a Hopf algebra defined by the 4-term relations if m>2. We des…