arXiv subjects

Stephan Wehrli

Publications and source records attributed to Stephan Wehrli.

5 recordsLinked to original sources

arXiv2026

A module structure on odd Khovanov homology and the odd invariant for ribbon 2-knots

We prove that the reduced odd Khovanov homology of a link $L$ is naturally a module over the exterior algebra of the first homology of the link's branched double-cover. We then describe this module structure more geometrically and related it to the odd Khovanov maps induced by link cobordisms. As an application, we will give a combinatorial proof of a recent result of Spyropoulos-Vidyarthi-Zhang about the odd invariant for $2$-knots in the special case where the $2$-knot is a ribbon $2$-knot. Additionally, we will show that Levine-Zemke's main result from their 2019 paper on Khovanov homology and ribbon concordance remains true for odd Khovanov homology with rational coefficients and with coefficients in $\mathbb{Z}_{2^k}$.

math.GT↗

arXiv2024

Functoriality of Odd and Generalized Khovanov Homology in $\mathbb{R}^3\times I$

We extend the generalized Khovanov bracket to smooth link cobordisms in $\mathbb{R}^3\times I$ and prove that the resulting theory is functorial up to global invertible scalars. The generalized Khovanov bracket can be specialized to both even and odd Khovanov homology. Particularly by setting $\pi=-1$, we obtain that odd Khovanov homology is functorial up to sign. We end by showing that odd Khovanov homology is not functorial under smooth link cobordisms in $S^3\times I$.

math.GT↗

arXiv2015

A combinatorial proof of the homology cobordism classification of lens spaces

It follows implicitly from recent work in Heegaard Floer theory that lens spaces are homology cobordant exactly when they are oriented homeomorphic. We provide a new combinatorial proof using the Heegaard Floer d-invariants, which themselves may be defined combinatorially for lens spaces.

math.GT↗

arXiv2008

On the Colored Jones Polynomial, Sutured Floer homology, and Knot Floer homology

Let K in S^3 be a knot, and let \widetilde{K} denote the preimage of K inside its double branched cover, Σ(K). We prove, for each integer n > 1, the existence of a spectral sequence from Khovanov's categorification of the reduced n-colored Jones polynomial of the mirror of K to the knot Floer homology of (Σ(K),\widetilde{K}) (when n odd) and to (S^3, K # K) (when n even). A corollary of our result is that Khovanov's categorification of the reduced n-colored Jones polynomial detects the unknot whenever n>1.

math.GT↗

arXiv2006

Categorification of the colored Jones polynomial and Rasmussen invariant of links

We define a family of formal Khovanov brackets of a colored link depending on two parameters. The isomorphism classes of these brackets are invariants of framed colored links. The Bar-Natan functors applied to these brackets produce Khovanov and Lee homology theories categorifying the colored Jones polynomial. Further, we study conditions under which framed colored link cobordisms induce chain transformations between our formal brackets. We conjecture that, for special choice of parameters, Khovanov and Lee homology theories of colored links are functorial (up to sign). Finally, we extend the Rasmussen invariant to links and give examples, where this invariant is a stronger obstruction to sliceness than the multivariable Levine-Tristram signature.

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