Related papers: Surfaces in 4-manifolds and the surgery conjecture

We introduce a relation of cobordism for knots in thickened surfaces and study cobordism invariants of such knots.

We study the cobordism of manifolds with boundary, and its applications to codimension 2 embeddings $M^m\subset N^{m+2}$, using the method of the algebraic theory of surgery. The first main result is a splitting theorem for cobordisms of…

The A-B slice problem, a reformulation of the 4-dimensional topological surgery conjecture for free groups, is shown to admit a link-homotopy+ solution. The proof relies on geometric applications of the group-theoretic 2-Engel relation.…

Using an obstruction based on Donaldson's theorem on the intersection forms of definite 4-manifolds, we determine which connected sums of lens spaces smoothly embed in S^4. We also find constraints on the Seifert invariants of Seifert…

This is a survey article about the connections between knot theory and four-dimensional topology. Every four-manifold can be represented in terms of a link, by a Kirby diagram. This point of view has led to progress in computing invariants…

The adjunction inequality is a key tool for bounding the genus of smoothly embedded surfaces in 4-manifolds. Using gauge-theoretic invariants, many versions of this inequality have been established for both closed surfaces and surfaces with…

We study the structure induced on a smooth manifold by a continuous selection of smooth functions. In case such selection is suitably generic, it provides a stratification of the manifold, whose strata are algebraically defined smooth…

We introduce a surgery for generalized complex manifolds whose input is a symplectic 4-manifold containing a symplectic 2-torus with trivial normal bundle and whose output is a 4-manifold endowed with a generalized complex structure…

We give an overview of various recent results concerning the topology of symplectic 4-manifolds and singular plane curves, using branched covers and isotopy problems as a unifying theme. While this paper does not contain any new results, we…

We show that any closed oriented 3-manifold can be topologically embedded in some simply-connected closed symplectic 4-manifold, and that it can be made a smooth embedding after one stabilization. As a corollary of the proof we show that…

The A-B slice problem is a reformulation of the topological 4-dimensional surgery conjecture in terms of decompositions of the 4-ball and link homotopy. We show that link groups, a recently developed invariant of 4-manifolds, provide an…

We propose a way to define and compute invariants of general smooth 4-manifolds based on topological twists of non-Lagrangian 4d N=2 and N=3 theories in which the problem is reduced to a fairly standard computation in topological A-model,…

Given an injective amalgam at the level of fundamental groups and a specific 3-manifold, is there a corresponding geometric-topological decomposition of a given 4-manifold, in a stable sense? We find an algebraic-topological splitting…

This article is concerned with locally flatly immersed surfaces in simply-connected $4$-manifolds where the complement of the surface has fundamental group $\mathbb{Z}$. Once the genus and number of double points are fixed, we classify such…

In this paper, we perform a detailed investigation on the various geometrical properties of trapped surfaces and the boundaries of trapped region in general relativity. This treatment extends earlier work on LRS II spacetimes to a general 4…

The main result of this paper states that a symplectic s-cobordism of elliptic 3-manifolds is diffeomorphic to a product (assuming a canonical contact structure on the boundary). Based on this theorem, we conjecture that a smooth…

We show that every plumbing of disc bundles over surfaces whose genera satisfy a simple inequality may be embedded as a convex submanifold in some closed hyperbolic four-manifold. In particular its interior has a geometrically finite…

In this note, we investigate the relation between double points and complex points of immersed surfaces in almost-complex 4-manifolds and show how estimates for the minimal genus of embedded surfaces lead to inequalities between the number…

In this paper we clarify an issue in the knot surgery construction of Fintushel and Stern. Using knot surgery, they construct an infinite number of smooth structures on 4-manifolds satisfying certain conditions, but they do not explicitly…

A multisection of a 4-manifold is a decomposition into 1-handlebodies intersecting pairwise along 3-dimensional handlebodies or along a central closed surface; this generalizes the Gay-Kirby trisections. We show how to compute the twisted…