Professor of Mathematics, University of Virginia.

Research interests: Low-dimensional geometry and topology

Read more aboutProfessor of Mathematics, University of Virginia.

Research interests: Low-dimensional geometry and topology

Read more about

Akhmechet R, Krushkal V, Willis M. Stable homotopy refinement of quantum annular homology. arXiv:2001.00077. 2020.Abstract

We construct a stable homotopy refinement of quantum annular homology, a link homology theory introduced by Beliakova, Putyra and Wehrli. For each r>2 we associate to an annular link L a naive Z/rZ-equivariant spectrum whose cohomology is isomorphic to the quantum annular homology of L as modules over Z[Z/rZ]. The construction relies on an equivariant version of the Burnside category approach of Lawson, Lipshitz and Sarkar. The quotient under the cyclic group action is shown to recover the stable homotopy refinement of annular Khovanov homology. We study spectrum level lifts of structural properties of quantum annular homology.

Fendley P, Krushkal V. Topological quantum field theory and polynomial identities for graphs on the torus. arXiv:1902.02760 . 2019.Abstract

We establish a relation between the trace evaluation in SO(3) topological quantum field theory and evaluations of a topological Tutte polynomial. As an application, a generalization of the Tutte golden identity is proved for graphs on the torus.

Freedman M, Krushkal V. Universal Surgery Problems with Trivial Lagrangian. Math. Res. Letters, to appear. 2019.Abstract

We study the effect of Nielsen moves and their geometric counterparts, handle slides, on good boundary links. A collection of links, universal for 4-dimensional surgery, is shown to admit Seifert surfaces with a trivial Lagrangian. They are good boundary links, with Seifert matrices of a more general form than in known constructions of slice links. We show that a certain more restrictive condition on Seifert matrices is sufficient for proving the links are slice. We also give a correction of a Kirby calculus identity in [FK2], useful for constructing surgery kernels associated to link-slice problems.

krushkal@virginia.edu

office: 321 Kerchof Hall

phone: (434) 924-4949

2020 By the Rector and Visitors of the University of Virginia | Report Copyright Infringement