Related papers: An odd Khovanov homotopy type
Asaeda, Przytycki and Sikora defined a generalization of Khovanov homology for links in $I$-bundles over compact surfaces. We prove that for a link $L\subset (-1,1)\times T^2$, the Asaeda-Przytycki-Sikora homology of $L$ has rank $2$ with…
We construct a zig-zag from the once delooped space of pseudoisotopies of a closed $2n$-disc to the once looped algebraic $K$-theory space of the integers and show that the maps involved are $p$-locally $(2n-4)$-connected for $n>3$ and…
We lift the characteristic-2 totally twisted Khovanov homology of Roberts and Jaeger to a theory with integer coefficients. The result is a complex computing reduced odd Khovanov homology for knots. This complex is equivalent to a…
Plamenevskaya defined an invariant of transverse links as a distinguished class in the even Khovanov homology of a link. We define an analog of Plamenevskaya's invariant in the odd Khovanov homology of Ozsv\'ath, Rasmussen, and Szab\'o. We…
We introduce a new version of symplectic annular Khovanov homology and establish spectral sequences from (i) the symplectic annular Khovanov homology of a knot to the link Floer homology of the lift of the annular axis in the double…
We show that the information contained in the associated graded vector space to Gornik's version of Khovanov-Rozansky knot homology is equivalent to a single even integer s_n(K). Furthermore we show that s_n is a homomorphism from the…
Combining results of Wahl, Galatius--Madsen--Tillmann--Weiss and Korkmaz one can identify the homotopy-type of the classifying space of the stable non-orientable mapping class group $N_\infty$ (after plus-construction). At odd primes p, the…
Lawrence Roberts, extending the work of Ozsvath-Szabo, showed how to associate to a link, L, in the complement of a fixed unknot, B, in S^3, a spectral sequence from the Khovanov homology of a link in a thickened annulus to the knot Floer…
Khovanov homology offers a nontrivial generalization of Jones polynomial of links in R^3 (and of Kauffman bracket skein module of some 3-manifolds). In this chapter (Chapter X) we define Khovanov homology of links in R^3 and generalize the…
We use categorical annular evaluation to give a uniform construction of both $\mathfrak{sl}_n$ and HOMFLYPT Khovanov-Rozansky link homology, as well as annular versions of these theories. Variations on our construction yield…
This paper extends the results of "Operads and Algebraic Homotopy" in giving algebraic invariants for the stable homotopy type of a pointed simply-connected simplicial set.
In this dissertation, we extend the odd Khovanov bracket to link cobordisms and prove that our construction is functorial up to sign. We then build an odd Khovanov theory for dotted link cobordisms. Out of the dotted theory, a module…
In view of the Segal construction each category with a coherent operation gives rise to a cohomology theory. Similarly each open stable differential relation $R$ imposed on smooth maps of manifolds determines cohomology theories $k^*$ and…
We define a third grading on Khovanov homology, which is an invariant of annular links but changes by $\pm 1$ under stabilization. We illustrate the use of our computer implementation, and give some example calculations.
Khovanov-Floer theories are a class of homological link invariants which admit spectral sequences from Khovanov homology. They include Khovanov homology, Szab{\'o}'s geometric link homology, singular instanton homology, and various Floer…
This paper begins with a survey of some applications of Khovanov homology to low-dimensional topology, with an eye toward extending these results to $\mathfrak{sl}(n)$ homologies. We extend Levine and Zemke's ribbon concordance obstruction…
We show that the Khovanov and Cooper-Krushkal models for colored sl(2) homology are equivalent in the case of the unknot, when formulated in the quantum annular Bar-Natan category. Again for the unknot, these two theories are shown to be…
Given a real arrangement $A$, the complement $M(A)$ of the complexification of $A$ admits an action of $\mathbb{Z}_2$ by complex conjugation. We define the equivariant Orlik-Solomon algebra of $A$ to be the $\mathbb{Z}_2$-equivariant…
Khovanov homology ist a new link invariant, discovered by M. Khovanov, and used by J. Rasmussen to give a combinatorial proof of the Milnor conjecture. In this thesis, we give examples of mutant links with different Khovanov homology. We…
We introduce an sl(n) homology theory for knots and links in the thickened annulus. To do so, we first give a fresh perspective on sutured annular Khovanov homology, showing that its definition follows naturally from trace…