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Creators/Authors contains: "Krushkal, Vyacheslav"

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  1. ; ; (, Mathematical Research Letters)
    Free, publicly-accessible full text available February 10, 2026
  2. ; ; (, Mathematical research letters)
    Free, publicly-accessible full text available February 10, 2026
  3. ; ; (, Bulletin of the London Mathematical Society)
    Abstract The universal pairing for manifolds was defined and shown to lack positivity in dimension 4 in [Freedman, Kitaev, Nayak, Slingerland, Walker, and Wang, J. Geom. Topol.9(2005), 2303–2317]. We prove an analogous result for 2‐complexes, and show that the universal pairing does not detect the difference between simple homotopy equivalence and 3‐deformations. The question of whether these two equivalence relations are different for 2‐complexes is the subject of the Andrews–Curtis conjecture. We also discuss the universal pairing for higher dimensional complexes and show that it is not positive. 
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  4. ; ; (, arXiv)
    Accepted Manuscript Full Text Available
  5. ; (, Asian Journal of Mathematics)
    Full Text Available 
  6. ; (, Indiana University Mathematics Journal)
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  7. ; (, Annales de l’Institut Henri Poincaré D)
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  8. ; ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    Abstract In this paper, an invariant is introduced for negative definite plumbed 3-manifolds equipped with a spin c {{}^{c}} -structure. It unifies and extends two theories with rather different origins and structures. One theory is lattice cohomology, motivated by the study of normal surface singularities, known to be isomorphic to the Heegaard Floer homology for certain classes of plumbed 3-manifolds. Another specialization gives BPS q -series which satisfy some remarkable modularity properties and recover SU ⁢ ( 2 ) {{\rm SU}(2)} quantum invariants of 3-manifolds at roots of unity.In particular, our work gives rise to a 2-variable refinement of the Z ^ {\widehat{Z}} -invariant. 
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  9. ; ; (, Advances in Mathematics)
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  10. ; ; (, Compositio Mathematica)
    null (Ed.)
    We construct a stable homotopy refinement of quantum annular homology, a link homology theory introduced by Beliakova, Putyra and Wehrli. For each $$r\geq ~2$$ we associate to an annular link $$L$$ a naive $$\mathbb {Z}/r\mathbb {Z}$$ -equivariant spectrum whose cohomology is isomorphic to the quantum annular homology of $$L$$ as modules over $$\mathbb {Z}[\mathbb {Z}/r\mathbb {Z}]$$ . 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. 
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