4 papers
K-theory of Jones polynomials
Andrey Glubokov, Igor Nikolaev
We recover the Jones polynomials of knots and links from the K-theory of a cluster C*-algebra of the sphere with two cusps. In particular, an interplay between the Chebyshev and Jo…
Subfactors and Hecke groups
Andrey Glubokov, Igor Nikolaev
We study a relation between the Hecke groups and the index of subfactors in a von Neumann algebra. Such a problem was raised by V. F. R. Jones. We solve the problem using the notio…
Jones Index Theorem revisited
Andrey Yu. Glubokov, Igor V. Nikolaev
We prove the Jones Index Theorem using the K-theory of a cluster -algebra of the Riemann sphere with two boundary components.
Ideals on the Quantum Plane's jet space
Andrey Glubokov
The goal of this paper is to introduce some rings that play the role of the jet spaces of the quantum plane and unlike the quantum plane itself possess interesting nontrivial prime…