arXiv research

Fintushel-Stern surgery on fibered knots in torus bundles yields symplectic manifolds.

We discuss some consequences Fintushel-Stern `knot surgery' operation on 4-manifolds coming from its handlebody description. We give some generalizations of this operation and give a counterexample to their conjecture.

We discuss the relation between Fintushel-Stern knot surgery operation on 4-manifolds and Scharlemann manifolds, and as a corollary show that they all are standard. Along the way we show that the fishtail can exotically knot in the 4-sphere infinitely many ways.

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 Matsumoto's $S^4$), then the knot surgery gives rise to standard manifolds. The …

In this article we prove that Fintushel-Stern's construction of Horikawa surface, which is obtained from an elliptic surface via a rational blow-down surgery in smooth category, can be performed in complex category. The main technique involved is Q-Gorenstein smoothings.

In this note we present a new definition of the 4-manifold admitting inequivalent symplectic structures constructed by McMullen-Taubes which leads to the identification of a new symplectic structure. We prove moreover that it is diffeomorphic to one of the link surgery manifolds introduced by Fintushel-Stern.

In this note we prove that, for any integer n, there exist a smooth 4-manifold, homotopic to a K3 surface, defined by applying the link surgery method of Fintushel-Stern to a certain 2-component graph link, which admits n inequivalent symplectic structures Keywords: Symplectic topology of 4-manifolds; Seiberg-Witten th…

Some generalizations and variations of the Fintushel-Stern rim surgery are known to produce smoothly knotted surfaces. We show that if the fundamental groups of their complements are cyclic, then these surfaces are topologically unknotted. Using a twist-spinning construction from high-dimensional knot theory, we constr…

New surfaces in 4-manifolds are created and shown to be diffeomorphic after stabilization.

In the previous paper the author defined an infinite order plug $(P,\varphi)$ which gives rise to infinite Fintushel-Stern's knot-surgeries. Here, we give two 4-dimensional infinitely many exotic families $Y_n$, $Z_n$ of exotic enlargements of the plug. The families $Y_n$, $Z_n$ have $b_2=3$, $4$ and the boundaries are…

New exotic 4-manifolds with even $b_2^+$ and $\mathbb{Z}/2\mathbb{Z}$ fundamental group.

Paper examines 4-manifold structures using chord assignments.

In 1987 S Cappell and J Shaneson constructed an s-cobordism H from the quaternionic 3-manifold Q to itself, and asked whether H or any of its covers are trivial product cobordism? In this paper we study H, and in particular show that its 8-fold cover is the product cobordism from S^3 to itself. We reduce the triviality…

Suppose that $C=(C_1,..., C_m)$ is a configuration of 2-dimensional symplectic submanifolds in a symplectic 4-manifold $(X,ω)$ with connected, negative definite intersection graph $Γ_C$. We show that by replacing an appropriate neighborhood of $\cup C_i$ with a smoothing $W_S$ of a normal surface singularity $(S, 0)$ w…

Let E(1)_K denote the closed 4-manifold that is homotopy equivalent (hence homeomorphic) to the rational elliptic surface E(1) and is obtained by performing Fintushel-Stern knot surgery on E(1) using a knot K in S^3. We construct an infinite family of homologous non-isotopic symplectic tori representing a primitive hom…

In this paper we prove several related results concerning smooth $\Z_p$ or $\s^1$ actions on 4-manifolds. We show that there exists an infinite sequence of smooth 4-manifolds $X_n$, $n\geq 2$, which have the same integral homology and intersection form and the same Seiberg-Witten invariant, such that each $X_n$ support…

We show that there is a well-defined cap-product structure on the Fintushel-Stern spectral sequence. Hence we obtain the induced cap-product structure on the ${\BZ}_8$-graded instanton Floer homology. The cap-product structure provides an essentially new property of the instanton Floer homology, from a topological poin…

The study restricts when Seifert fibered spaces can bound definite manifolds.

Fintushel and Stern have proved that if S \subset X is a symplectic surface in a symplectic 4-manifold such that S has simply-connected complement and nonnegative self-intersection, then there are infinitely many topologically equivalent but smoothly distinct embedded surfaces homologous to S. Here we extend this resul…

Surface corks modify 4-manifold structures without changing their homeomorphism type.

We determine the smooth concordance order of the 3-stranded pretzel knots P(p,q,r) with p,q,r odd. We show that each one of finite order is, in fact, ribbon, thereby proving the slice-ribbon conjecture for this family of knots. As corollaries we give new proofs of results first obtained by Fintushel-Stern and Casson-Go…

New knots have unique Whitehead doubles.

In this paper, we investigate existence of inequivalent smooth structures on closed smooth non-orientable 4-manifolds building upon results of Akbulut, Cappell-Shaneson, Fintushel-Stern, Gompf, and Stolz. We add to the number of known constructions and provide new examples of exotic manifolds that are obtained as an ap…

The rational homology balls $B_n$ appeared in Fintushel and Stern's rational blow-down construction [FS] and were subsequently used (e.g. Fintushel-Stern[FS4], Park[Pa2]) to construct exotic smooth manifolds with small Euler numbers. We show that a large class of smooth 4-manifolds have all of the $B_n$'s for odd $n \g…

In this paper, we derive the family switching formula of -n two-sphere fiber bundle embedded in a smooth four-manifold fiber bundle. In the smooth category, it is a partial generalization of Fintushel-Stern's argument for four-manifolds. We also derive an algebraic analogue of the family switching formula, allowing the…

We construct an invariant for non-spin 4-manifolds by using 2-torsion cohomology classes of moduli spaces of instantons on SO(3)-bundles. The invariant is an SO(3)-version of Fintushel-Stern's 2-torsion instanton invariant. We show that this SO(3)-torsion invariant is non-trivial for $2CP^2 # -CP^2$, while it is known …

We introduce several new families of relations in the mapping class groups of planar surfaces, each equating two products of right-handed Dehn twists. The interest of these relations lies in their geometric interpretation in terms of rational blowdowns of 4-manifolds, specifically via monodromy substitution in Lefschet…

Formula connects surgeries to Seiberg-Witten invariants.

Let K be a knot in the 3--sphere. An r-surgery on K is left-orderable if the resulting 3--manifold K(r) of the surgery has left-orderable fundamental group, and an r-surgery on K is called an L-space surgery if K(r) is an L-space. A conjecture of Boyer, Gordon and Watson says that non-reducing surgeries on K can be cla…

Study confirms contact cosmetic surgery for most knots, with exceptions.

Study cosmetic surgeries on knots in homology spheres using Casson-Walker invariant.

A function Γ_Y relates Chern-Simons functional to homology cobordism invariants.

Cosmetic surgeries on pretzel knots are unique.

Study pochette surgery on 4-manifolds, focusing on 4-spheres.

We solve a conjecture about surgeries on special 3D shapes.

We formulate a very general conjecture relating the analytical invariants of a normal surface singularity to the Seiberg-Witten invariants of its link provided that the link is a rational homology sphere. As supporting evidence, we establish its validity for a large class of singularities: some rational and minimally e…

New method proves cosmetic surgery conjecture for certain knots.

New Heegaard Floer homology findings block chirally cosmetic surgeries.

Round surgery diagrams represent 3-manifolds in $S^3$.

The study calculates and analyzes alternating surgeries for various knots.

The LMO invariant helps find constraints for cosmetic surgeries on knots.

The paper constructs homotopy 4-spheres using pochette surgery.

Study chirally cosmetic surgeries on knots with constraints and invariants.

Contact round surgeries on $(\mathbb{S}^3,ξ_{st})$ help in constructing and understanding contact 3-manifolds.

This paper concerns the truly or purely cosmetic surgery conjecture. We give a survey on exceptional surgeries and cosmetic surgeries. We prove that the slope of an exceptional truly cosmetic surgery on a hyperbolic knot in $S^3$ must be $\pm 1$ and the surgery must be toroidal but not Seifert fibred. As consequence we…

Complete exceptional surgeries identified for two-bridge links.

New result on contact surgeries and overtwistedness.

Study classifies exceptional surgeries on specific links.