Related papers: A note on the concordance invariant epsilon
Dai, Hom, Stoffregen and Truong defined a family of concordance invariants $\varphi_j$. The example of a knot with zero Upsilon invariant but nonzero epsilon invariant previously given by Hom also has nonzero phi invariant. We show there…
Hom gives an example of a knot with vanishing Upsilon invariant but nonzero epsilon invariant. We build more such knots that are linearly independent in the smooth concordance group.
In this paper we construct an infinite family of knots with vanishing Upsilon invariant $\Upsilon$, although their secondary Upsilon invariants $\Upsilon^2$ show that they are linearly independent in the smooth knot concordance group. We…
Ozsvath-Stipsicz-Szabo recently defined a one-parameter family, upsilon of K at t, of concordance invariants associated to the knot Floer complex. We compare their invariant to the {-1, 0, 1}-valued concordance invariant epsilon, which is…
We extend the construction of upsilon-type invariants to null-homologous knots in rational homology three-spheres. By considering $m$-fold cyclic branched covers with $m$ a prime power, this extension provides new knot concordance…
We construct smooth concordance invariants of knots which take the form of piecewise linear maps from [0,1] to R, one for each n greater than or equal to 2. These invariants arise from sl(n) knot cohomology. We verify some properties which…
The knot concordance invariant Upsilon, recently defined by Ozsvath, Stipsicz, and Szabo, takes values in the group of piecewise linear functions on the closed interval [0,2]. This paper presents a description of one approach to defining…
The knot invariant Upsilon, defined by Ozsvath, Stipsicz, and Szabo, induces a homomorphism from the smooth knot concordance group to the group of piecewise linear functions on the interval [0,2]. Here we define a set of related secondary…
The Upsilon invariant of a knot is a concordance invariant derived from knot Floer homology theory. It is a piecewise linear continuous function defined on the interval $[0,2]$. Borodzik and Hedden gave a question asking for which knots the…
We define a new smooth concordance homomorphism based on the knot Floer complex and an associated concordance invariant, epsilon. As an application, we show that an infinite family of topologically slice knots are independent in the smooth…
By considering a version of Khovanov homology incorporating both the Lee and $E(-1)$ differentials, we construct a $1$-parameter family of concordance homomorphisms similar to the Upsilon invariant from knot Floer homology. This invariant…
To a region $C$ of the plane satisfying a suitable convexity condition we associate a knot concordance invariant $\Upsilon^C$. For appropriate choices of the domain this construction gives back some known knot Floer concordance invariants…
Two Heegaard Floer knot complexes are called stably equivalent if an acyclic complex can be added to each complex to make them filtered chain homotopy equivalent. Hom showed that if two knots are concordant, then their knot complexes are…
The Upsilon invariant is a concordance invariant in knot Floer homology. F\"{o}ldv\'{a}ri reconstructed the Upsilon invariant using grid homology. We prove that the Upsilon invariant in knot Floer homology and one in grid homology are…
The $\Upsilon$ invariant is a concordance invariant defined by using knot Floer homology. F\"{o}ldv\'{a}ri gives a combinatorial restructure of it using grid homology. We extend the combinatorial $\Upsilon$ invariant for balanced spatial…
According to the idea of Ozsv\'ath, Stipsicz and Szab\'o, we define the knot invariant $\Upsilon$ without the holomorphic theory, using constructions from grid homology. We develop a homology theory using grid diagrams, and show that…
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…
We give a formula of the Upsilon invariant of any L-space cable knot $K_{p,q}$ using $p,\Upsilon_K$ and $\Upsilon_{T_{p,q}}$. The integral value of the Upsilon invariant gives a ${\mathbb Q}$-valued knot concordance invariant. We compute…
We produce infinite families of knots $\{K^i\}_{i\geq 1}$ for which the set of cables $\{K^i_{p,1}\}_{i,p\geq 1}$ is linearly independent in the knot concordance group. We arrange that these examples lie arbitrarily deep in the solvable and…
Concordance invariants of knots are derived from the instanton homology groups with local coefficients, as introduced in earlier work of the authors. These concordance invariants include a 1-parameter family of homomorphisms $f_{r}$, from…