相关论文: Constructions of Smooth 4-Manifolds

We construct smooth manifolds with order two $\pi_1$ and even intersection forms which are irreducible, meaning they do not decompose into non-trivial connected sums. Their intersection forms being even implies that their universal covers…

Attaching a Casson handle to a slice disk complement yields a smooth 4-manifold that is homeomorphic to $\mathbb{R}^4$. We show that if two slice knots have sufficiently different knot Floer homology, then the resulting exotic…

This is a short survey on finite-volume hyperbolic four-manifolds. We describe some general theorems and focus on the concrete examples that we found in the literature. The paper contains no new result.

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…

We show that every smooth, closed, orientable 4-manifold X admits a special kind of handlebody decomposition that we call horizontal. We classify the closed 4-manifolds with the simplest horizontal decompositions and we describe all such…

We show that any topological, closed, oriented, non-spin $4$-manifold with fundamental group $\mathbb{Z}_{4k}$ and $\min(b_2^+, b_2^-)\geq 15$, has either none or infinitely many distinct smooth structures. Furthermore, we construct…

We build a non-compact, orientable, hyperbolic four-manifold of finite volume that does not admit any spin structure.

The content of this unpublished paper is subsumed in successive work of the authors, in particular arXiv:1102.0820, arXiv:1102.0821 and arXiv:1205.2434.

We classify small contractions of (holomorphically) symplectic 4-folds.

We show that there exists an exotic pair of $4$-manifolds with boundary whose trisection genera are $4$. We also construct genus-$3$ relative trisections for an infinite family of contractible $4$-manifolds introduced by Akbulut and Kirby.

We construct Anosov diffeomorphisms on manifolds that are homeomorphic to infranilmanifolds yet have exotic smooth structures. These manifolds are obtained from standard infranilmanifolds by connected summing with certain exotic spheres.…

We prove that any two smooth h-cobordant simply-connected 4-manifolds can be obtained by taking two manifolds with boundary, one of which is contractible, and gluing them along the boundary via two different attaching maps.

We construct complete, finite volume, 4-dimensional manifolds with sectional curvature $-1<K<0$ with cusp cross sections compact solvmanifolds.

We construct infinite families of topologically isotopic but smoothly distinct knotted spheres in many simply connected 4-manifolds that become smoothly isotopic after stabilizing by connected summing with $S^2 \times S^2$, and as a…

We define family versions of the invariant of 4-manifolds with contact boundary due to Kronheimer and Mrowka and use these to detect exotic diffeomorphisms of 4-manifolds with boundary. Further, we show the existence of the first example of…

This is a survey article on symplectically aspherical manifolds. The paper contains a discussion on constructions of symplectically aspherical manifolds, their topological properties and the role of this class in symplectic topology.…

We give a survey of geometric approaches to the topological 4-dimensional surgery and 5-dimensional s-cobordism conjectures, with a focus on the study of surfaces in 4-manifolds. The geometric lemma underlying these conjectures is a…

We describe special Ka\"hler geometry, special quaternionic manifolds, and very special real manifolds and analyze the structure of their isometries. The classification of the homogeneous manifolds of these types is presented.

In this paper, Problem 4.17 on R. Kirby's problem list is solved by constructing infinitely many aspherical 4-manifolds that are homology 4-spheres

This article analyzes the interplay between symplectic geometry in dimension four and the invariants for smooth four-manifolds constructed using holomorphic triangles introduced in math.SG/0110169. Specifically, we establish a non-vanishing…