Related papers: On the slice genus of links

A knot in the 3-sphere is called doubly slice if it is a slice of an unknotted 2-sphere in the 4-sphere. We give a bi-sequence of new obstructions for a knot being doubly slice. We construct it following the idea of Cochran-Orr-Teichner's…

For $\ell >1$, we develop $L^{(2)}$-signature obstructions for $(4\ell-3)$-dimensional knots with metabelian knot groups to be doubly slice. For each $\ell>1$, we construct an infinite family of knots on which our obstructions are non-zero,…

We construct a family of hyperbolic link complements by gluing tangles along totally geodesic four-punctured spheres, then investigate the commensurability relation among its members. Those with different volume are incommensurable,…

We investigate the nonorientable 4-genus $\gamma_4$ of a special family of 2-bridge knots, the twist knots and double twist knots $C(m,n)$. Because the nonorientable 4-genus is bounded by the nonorientable 3-genus, it is known that…

We give a complete characterization of the topological slice status of odd 3-strand pretzel knots, proving that an odd 3-strand pretzel knot is topologically slice if and only if either it is ribbon or has trivial Alexander polynomial. (By…

We use twisted Alexander polynomials to show that certain algebraically slice 2-bridge knots are not topologically slice, even though all prime power Casson-Gordon signatures vanish. We also provide some computations indicating the efficacy…

We introduce and study the notion of equivariant $\mathbb{Q}$-sliceness for strongly invertible knots. On the constructive side, we prove that every Klein amphichiral knot, which is a strongly invertible knot admitting a compatible negative…

We construct analogs of Khovanov-Jacobsson classes and the Rasmussen invariant for links in the boundary of any smooth oriented 4-manifold. The main tools are skein lasagna modules based on equivariant and deformed versions of…

Based on work of Rasmussen, we construct a concordance invariant associated to the knot Floer complex, and exhibit examples in which this invariant gives arbitrarily better bounds on the 4-ball genus than the Ozsvath-Szabo tau invariant.

Given a diagram D of a knot K, we give easily computable bounds for Rasmussen's concordance invariant s(K). The bounds are not independent of the diagram D chosen, but we show that for diagrams satisfying a given condition the bounds are…

For a knot $K$ in the 3-sphere and a simply connected closed 4-manifold $X$, we define the $X$-double slice genus of $K$, extending the notion from the case when $X$ is the 4-sphere. We show that for each integer $n$, there exists an…

The ``Links-Gould invariant'' is a two-variable Laurent polynomial invariant of oriented (1,1) tangles, which is derived from the representation of the braid generator associated with the one-parameter family of four dimensional…

We define a notion of complexity for shake-slice knots which is analogous to the definition of complexity for h-cobordisms studied by Morgan-Szab\'o. We prove that for each framing $n \ne 0$ and complexity $c \ge 0$, there is an…

We consider the ways in which a 4-tangle T inside a unit cube can be extended outside the cube into a knot or link L. We present two links n(T) and d(T) such that the greatest common divisor of the determinants of these two links always…

We define an annular concordance invariant and study its properties. When specialized to braids, this invariant gives bounds on band rank. We introduce a modified chain complex to reformulate the invariant. Then, by focusing on a special…

We use techniques of Freedman and Teichner to prove that, under certain circumstances, the multi-infection of a slice link is again slice (not necessarily smoothly slice). We provide a general context for proving links are slice that…

The Benard-Conway invariant of links in the 3-sphere is a Casson-Lin type invariant defined by counting irreducible SU(2) representations of the link group with fixed meridional traces. For two-component links with linking number one, the…

We show that the Casson knot invariant, linking number and Milnor's triple linking number, together with a certain 2-string link invariant $V_2$, are necessary and sufficient to express any string link Vassiliev invariant of order two.…

New lower bounds on the unknotting number of a knot are constructed from the classical knot signature function. These bounds can be twice as strong as previously known signature bounds. They can also be stronger than known bounds arising…

An estimate for the genus function in circle bundles over irreducible 3-manifolds is proven. This estimate is in many cases an equality and it relates the minimal genus of the surfaces representing a given homology class with the…