Related papers: Smoothly knotted surfaces that remain distinct aft…

We classify topological $4$-manifolds with boundary and fundamental group $\mathbb{Z}$, under some assumptions on the boundary. We apply this to classify surfaces in simply-connected $4$-manifolds with $S^3$ boundary, where the fundamental…

In this paper we will show that two surfaces of the same genus and homology class in a simply connected 4-manifold are concordant. We will show they are often topologically isotopic when their complements have cyclic fundamental group.…

In this paper we show that there exist simply connected symplectic 4-manifolds which contain infinitely many knotted lagrangian tori, i.e. lagrangian embeddings of tori that are homotopic but not isotopic. Moreover, the homology class they…

Given an embedded stable hypersurface in a four-dimensional symplectic manifold, we prove that it is stable isotopic to a $C^0$-close stable hypersurface with the following property: $C^\infty$-nearby hypersurfaces are generically unstable.…

In this paper we exhibit infinite families of embedded tori in 4-manifolds that are topologically isotopic but smoothly distinct. The interesting thing about these tori is that they are topologically trivial in the sense that each bounds a…

We compare two naturally arising notions of unknotting number for 2-spheres in the 4-sphere: namely, the minimal number of 1-handle stabilizations needed to obtain an unknotted surface, and the minimal number of Whitney moves required in a…

We prove necessary and sufficient conditions for a smooth surface in a 4-manifold X to be pseudoholomorphic with respect to some almost complex structure on X. This provides a systematic approach to the construction of pseudoholomorphic…

A knitted surface is a surface with or without closed components smoothly properly embedded in $D^2 \times B^2$, which is a generalization of a braided surface. A knitted surface is called a 2-dimensional knit if its boundary is the closure…

For any link in the $3$-sphere, we give a visual construction of a stable map $f$ from the $3$-sphere into the real plane enjoying the following properties; $f$ has no cusp point, the set of definite fold points of $f$ is isotopic to the…

We prove a lower bound for the first Steklov eigenvalue of embedded minimal hypersurfaces with free boundary in a compact $n$-dimensional manifold which has nonnegative Ricci curvature and strictly convex boundary. When $n=3$, this implies…

We introduce an information-theoretic framework for smooth structures on topological manifolds, replacing coordinate charts with small-scale entropy data of local probability probes. A concise set of axioms identifies admissible coordinate…

We study how to construct explicit deformations of generic smooth maps from closed $n$--dimensional manifolds $M$ with $n \geq 2$ to the $2$--sphere $S^2$ and show that every smooth map $M \to S^2$ is homotopic to a $C^\infty$ stable map…

In this paper we study smooth structures on closed oriented 4-manifolds with fundamental group Z_2 and definite intersection form. We construct infinitely many irreducible, smooth, oriented, closed, definite four-manifolds with fundamental…

Homological stability for sequences of groups is often proved by studying the spectral sequence associated to the action of a typical group in the sequence on a highly-connected simplicial complex whose stabilizers are related to previous…

We give an elementary obstruction to reducibility for knotted surfaces in the four-sphere. As a new application, we construct stably irreducible non-orientable surfaces.

Let $W$ be a compact smooth $4$-manifold that deformation retract to a PL embedded closed surface. One can arrange the embedding to have at most one non-locally-flat point, and near the point the topology of the embedding is encoded in the…

We investigate constraints on embeddings of a non-orientable surface in a $4$-manifold with the homology of $M \times I$, where $M$ is a rational homology $3$-sphere. The constraints take the form of inequalities involving the genus and…

We prove that the homology of the mapping class group of any 3-manifold stabilizes under connected sum and boundary connected sum with an arbitrary 3-manifold when both manifolds are compact and orientable. The stabilization also holds for…

Under a simple assumption on Seifert surfaces, we characterise knots whose stable topological 4-genus coincides with the genus.

Conjecturally, a knot is slice if and only if its positive Whitehead double is slice. We consider an analogue of this conjecture for slice disks in the four-ball: two slice disks of a knot are smoothly isotopic if and only if their positive…