Related papers: Alternating Surgeries

It is known that each of the successive quotient groups of the grope and solvable filtrations of the knot concordance group has an infinite rank subgroup. The generating knots of these subgroups are constructed using iterated doubling…

Building on Greene's changemaker lattices, we develop a lattice embedding obstruction to realizing an L-space bounding a definite 4-manifold as integer surgery on a knot in the Poincar\'e homology sphere. As the motivating application, we…

We show that any knot which is smoothly the closure of a 3-braid cannot be Lagrangian concordant to and from the maximum Thurston-Bennequin Legendrian unknot except the unknot itself. Our obstruction comes from drawing the Weinstein…

Fintushel-Stern's knot surgery gave many pairs of exotic manifolds, which are homeomorphic but non-diffeomorphic. We show that if an elliptic fibration has two parallel, oppositely oriented vanishing circles (for example $S^2\times S^2$ or…

A persistent lamination for a knot K is an essential lamination in the complement of K, which remains essential after every non-trivial Dehn surgery along K. Having a persistent lamination implies, for example, that every manifold obtained…

We examine surgery on a knot in $S^3$ to determine surgery obstructions to Seifert fibered integral homology spheres. We find such surgery obstructions using Heegaard Floer, Knot Floer homology and the mapping cone formula for computing…

We compute the $\text{PSL}(2,\mathbb{C})$ Chern-Simons partition function of a closed 3-manifold obtained from Dehn fillings of the link complement $\mathbf S^3\backslash {\mathcal{L}}$, where $\mathcal{L}=\mathcal{K}# H$ is the connected…

Let $M_K$ be the 2-fold branched cover of a knot $K in $S^3$. If $H_1(M_K) = {\bf Z}_3 \oplus {\bf Z}_{3^{2i}} \oplus G$ where 3 does not divide the order of $G$ then $K$ is not of order 4 in the concordance group. This obstruction detects…

Suppose $\alpha$ and $R$ are disjoint simple closed curves in the boundary of a genus two handlebody $H$ such that $H[R]$ embeds in $S^3$ as the exterior of a hyperbolic knot $k$(thus, $k$ is a tunnel-number-one knot), and $\alpha$ is…

We show that for any nontrivial knot in $S^3$, there is an open interval containing zero such that a Dehn surgery on any slope in this interval yields a 3-manifold with taut foliations. This generalizes a theorem of Gabai on zero frame…

In this paper, we study alternating links in thickened surfaces in terms of the lattices of integer flows on their Tait graphs. We use this approach to give a short proof of the first two generalised Tait conjectures. We also prove that the…

We describe an algorithm to find ribbon disks for alternating knots, and the results of a computer implementation of this algorithm. The algorithm is underlain by a slice link obstruction coming from Donaldson's diagonalisation theorem. It…

Strongly-cyclic branched coverings of knots are studied by using their (g,1)-decompositions. Necessary and sufficient conditions for the existence and uniqueness of such coverings are obtained. It is also shown that their fundamental groups…

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…

We use the immersed curves description of bordered Floer homology to study $d$-invariants of double branched covers $\Sigma_2(L)$ of arborescent links $L \subset S^3$. We define a new invariant $\Delta_{sym}$ of bordered…

We consider the problem of deforming simultaneously a pair of given structures. We show that such deformations are governed by an L-infinity algebra, which we construct explicitly. Our machinery is based on Th. Voronov's derived bracket…

We introduce explicit holonomy perturbations of the Chern-Simons functional on a 3-ball containing a pair of unknotted arcs. These perturbations give us a concrete local method for making the moduli spaces of flat singular SO(3) connections…

We define an obstruction for a knot to be Z[Z]-homology ribbon, and use this to provide restrictions on the integers that can occur as the triple linking numbers of derivative links of knots that are either homotopy ribbon or doubly slice.…

This work identifies a class of moves on knots which translate to $m$-equivalences of the associated $p$-fold branched cyclic covers, for a fixed $m$ and any $p$ (with respect to the Goussarov-Habiro filtration.) These moves are applied to…

We discuss 3-manifolds which are cyclic coverings of the 3-sphere, branched over 2-bridge knots and links. Different descriptions of these manifolds are presented: polyhedral, Heegaard diagram, Dehn surgery and coloured graph constructions.…