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Introduction
Subhankar Dey currently is a Postdoc in the Department of Mathematical Sciences, Durham University.
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Publications
Publications (9)
We prove that the $(p,q)$-cable of a non-trivial knot is not Floer homologically thin. Using this and a theorem of Ian Zemke in \cite{zemke}, we find a larger class of satellite knots, containing non-cable knots as well, which are not Floer homologically thin.
We show that there exists an algorithm that takes as input two closed, simply connected, topological 4-manifolds and decides whether or not these 4-manifolds are homeomorphic. In particular, we explain in detail how closed, simply connected, topological 4-manifolds can be naturally represented by a Kirby diagram consisting only of 2-handles. This r...
Martin showed that link Floer homology detects braid axes. In this paper we extend this result to give a topological characterisation of links which are almost braided from the point of view of link Floer homology. The result is inspired by work of Baldwin-Sivek and Li-Ye on nearly fibered knots. Applications include that Khovanov homology detects...
Viewing the BRAID invariant as a generator of link Floer homology, we generalize work of Baldwin–Vela-Vick to obtain rank bounds on the next-to-top grading of knot Floer homology. These allow us to classify links with knot Floer homology of rank at most eight and prove a variant of a classification of links with Khovanov homology of low rank due to...
We apply sutured Floer homology techniques to study the knot and link Floer homologies of various links with annuli embedded in their exteriors. Our main results include, for large $m$, characterizations of links with the same link Floer homology as $(n,nm)$-cables of $L$-space knots or the same knot Floer homology as $(2,2m)$-cables of $L$-space k...
Viewing the BRAID invariant as a generator of link Floer homology we generalise work of Baldwin-Vela-Vick to obtain rank bounds on the next to top grading of knot Floer homology. These allow us to classify links with knot Floer homology of rank at most eight, and prove a variant of a classification of links with Khovanov homology of low rank due to...
In this paper, we give a combinatorial description of the concordance invariant $\varepsilon$ defined by Hom in \cite{hom2011knot}, prove some properties of this invariant using grid homology techniques. We also compute $\varepsilon$ of $(p,q)$ torus knots and prove that $\varepsilon(\mathbb{G}_+)=1$ if $\mathbb{G}_+$ is a grid diagram for a positi...
