相关论文: New obstructions to doubly slicing knots

Using the knot Floer homology filtration, we define invariants associated to a knot in a three-manifold possessing non-vanishing Floer co(homology) classes. In the case of the Ozsvath-Szabo contact invariant we obtain an invariant of knots…

Using spinning we analyze in a geometric way Haefliger's smoothly knotted (4k-1)-spheres in the 6k-sphere. Consider the 2-torus standardly embedded in the 3-sphere, which is further standardly embedded in the 6-sphere. At each point of the…

We study the group of rational concordance classes of codimension two knots in rational homology spheres. We give a full calculation of its algebraic theory by developing a complete set of new invariants. For computation, we relate these…

We prove that an odd pretzel knot is doubly slice if it has $2n+1$ twist parameters consisting of $n+1$ copies of $a$ and $n$ copies of $-a$ for some odd integer $a$. Combined with the work of Issa and McCoy, it follows that these are the…

A pretzel knot $K$ is called $odd$ if all its twist parameters are odd, and $mutant$ $ribbon$ if it is mutant to a simple ribbon knot. We prove that the family of odd, 5-stranded pretzel knots satisfies a weaker version of the Slice-Ribbon…

By examining the homology groups of a 4-manifold associated to an integral surgery on a knot $K$ in a rational homology 3-sphere $Y$ yielding a rational homology 3-sphere $Y^*$ with surgery dual knot $K^*$, we show that the subgroups…

In this paper, we study a special family of $(1,1)$ knots called constrained knots, which includes 2-bridge knots in the 3-sphere $S^3$ and simple knots in lens spaces. Constrained knots are parameterized by five integers and characterized…

Let $\mathcal{T}$ be the group of smooth concordance classes of topologically slice knots, and $\{0\}\subset\cdots\subset \mathcal{T}_{n+1}\subset\mathcal{T}_{n}\subset \cdots\subset \mathcal{T}_{0}\subset \mathcal{T}$ be the bipolar…

Hom and Wu introduced the knot concordance invariant $\nu^{+}$ for knots in $S^{3}$ and proved that it gives a lower bound for the slice genus. Wu and Yang extended $\nu^{+}$ to knots in rational homology $3$-spheres, where it gives a lower…

We define a filtration of the smooth concordance group based on the genus of representative knots. We use the Heegaard Floer epsilon and Upsilon invariants to prove the quotient groups with respect to this filtration are infinitely…

By studying the Heegaard Floer homology of the preimage of a knot K in S^3 inside its double branched cover, we develop simple obstructions to K having finite order in the classical smooth concordance group. As an application, we prove that…

We describe an action of the concordance group of knots in the three-sphere on concordances of knots in arbitrary 3-manifolds. As an application we define the notion of almost-concordance between knots. After some basic results, we prove…

We review the polynomial parameterization of classical knots and prove the analogous results for long $2$ knots. We also construct polynomial parameterizations for certain classes of knotted spheres (such as spun and twist spun of the…

We study the double slice genus of a knot, a natural generalization of slice genus. We define a notion called band number, a natural generalization of band unknotting number, and prove it is an upper bound on double slice genus. Our bound…

We show that the subgroup of the knot concordance group generated by links of isolated complex singularities intersects the subgroup of algebraically slice knots in an infinite rank subgroup.

Using Taubes' periodic ends theorem, Auckly gave examples of toroidal and hyperbolic irreducible integer homology spheres which are not surgery on a knot in the three-sphere. We give an obstruction to a homology sphere being surgery on a…

For all n > 0 there is a homomorphism from the smooth concordance group of knots in dimension 2n + 1 to an algebraically defined group called the rational algebraic concordance group. This algebraic concordance group splits as a direct sum…

We give a method for constructing many pairs of distinct knots $K_0$ and $K_1$ such that the two 4-manifolds obtained by attaching a 2-handle to $B^4$ along $K_i$ with framing zero are diffeomorphic. We use the d-invariants of Heegaard…

Squeezed knots are those knots that appear as slices of genus-minimizing oriented smooth cobordisms between positive and negative torus knots. We show that this class of knots is large and discuss how to obstruct squeezedness. The most…

Prime power fold cyclic branched covers along smoothly slice knots all bound rational homology balls. This phenomenon, however, does not characterize slice knots. In this paper, we give a new construction of non-slice knots that have the…