Related papers: Notes on the knot concordance invariant Upsilon

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…

Using the theory of involutive Heegaard Floer knot theory developed by Hendricks-Manolescu, we define two involutive analogs of the Upsilon knot concordance invariant of Ozsvath-Stipsicz-Szabo. These involutive invariants are piecewise…

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…

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 study the behavior of $\Upsilon_K(t)$ under the cabling operation, where $\Upsilon_K(t)$ is the knot concordance invariant defined by Ozsv\'ath, Stipsicz, and Szab\'o, associated to a knot $K\subset S^3$. The main result…

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 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…

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.

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…

We provide explicit formulas for the integer-valued smooth concordance invariant $\upsilon(K) = \Upsilon_K(1)$ for every 3-braid knot $K$. We determine this invariant, which was defined by Ozsv\'ath, Stipsicz and Szab\'o, by constructing…

We introduce deformations of lattice cohomology corresponding to the knot homologies found by Ozsv\' ath, Stipsicz and Szab\' o in \cite{OSS4}. By means of holomorphic triangles counting, we prove equivalence with the analytic theory for a…

We compare the smooth concordance invariants Upsilon, phi and epsilon. Previous work gave examples of knots with one of the Upsilon and phi invariants zero but the epsilon invariant nonzero. We build an infinite family of linearly…

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…

Heegaard Floer theory produces chain complexes associated to knots. Viewed as modules over polynomial rings, such complexes yield torsion invariants that offer constraints on cobordisms between knots. For instance, Juhasz, Miller and Zemke…

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…

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…

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…

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…

Upsilon is a homomorphism on the smooth concordance group of knots defined by Ozsv\'{a}th, Stipsicz and Szab\'{o}. In this paper, we define a generalization of upsilon for a family of embedded graphs in rational homolog spheres. We show…

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…