Related papers: Compact 4-manifolds admitting special handle decom…

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…

We complete the classification of the smooth, closed, oriented 4-manifolds having Euler characteristic less than four and a horizontal handlebody decomposition of genus one. We use the classification result to find a large family of…

The aim of this paper is twofold. On the one hand, it provides a review of the links between random tensor models, seen as quantum gravity theories, and the PL-manifolds representation by means of edge-colored graphs (crystallization…

We construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented, parametrized two-manifold a differential graded algebra. For a three-manifold with parametrized boundary, the invariant comes…

For oriented manifolds of dimension at least 4 that are simply connected at infinity, it is known that end summing is a uniquely defined operation. Calcut and Haggerty showed that more complicated fundamental group behavior at infinity can…

We show that the simply-connected four-manifolds which admit locally linear, homologically trivial actions by rank two finite abelian groups are homeomorphic to connected sums of CP^2, -CP^2, and S^2 x S^2 (with one exception: pseudofree…

Internal stabilization adds a trivial handle to an embedded surface in a coordinate chart. It is known that any pair of smoothly knotted surfaces in a simply-connected $4$-manifold become smoothly isotopic after sufficiently many internal…

We present new explicit decompositions of manifolds via so-called fold maps into lower dimensional spaces. Fold maps form a nice class of so-called generic maps, generalizing Morse functions naturally. To understand the topologies and the…

Let $M$ be a triangulated, oriented, connected compact $3$-manifold with connected non-empty boundary. Such a manifold admits a unique decomposition into $\triangle$-prime $3$-manifolds. In this paper, we show that the adjoint Reidemeister…

Recently Gay and Kirby described a new decomposition of smooth closed $4$-manifolds called a trisection. This paper generalises Heegaard splittings of $3$-manifolds and trisections of $4$-manifolds to all dimensions, using triangulations as…

This} paper presents relations between least area and normal surfaces, embedded in either a Euclidean or hyperbolic $3$-manifold. A relaxed version of normal surfaces, termed quasi-normal, is introduced, and it is shown that under…

The present paper follows the computational approach to 3-manifold classification via edge-coloured graphs, already performed by several authors with respect to orientable 3-manifolds up to 28 coloured tetrahedra, non-orientable 3-manifolds…

We present a few general results on foliations of 4-manifolds by surfaces: existence, tautness, relations to minimal genus of embedded surfaces; as well as some open problems. We hope to stimulate interest in this area.

Given a simply-connected 4-manifold with boundary the 3-sphere, this paper establishes sufficient conditions for a knot in the boundary to be sliced by a locally flat disc in the 4-manifold, whose complement has finite cyclic fundamental…

Several new combinatorial descriptions of closed 4-manifolds have recently been introduced in the study of smooth maps from 4-manifolds to surfaces. These descriptions consist of simple closed curves in a closed, orientable surface and…

Let M be a connected orientable 3-manifold, and F a compact connected orientable surface properly embedded in M. If F cuts M into two connected 3-manifolds X and Y, that is, M=X \cup_F Y, we say that M is an amalgamation of X and Y along F;…

In this paper, we study the compactness of a boundary value problem for hyperkaehler 4-manifolds. We show that under certain topological conditions and the positive mean curvature condition on the boundary, a sequence of hyperkaehler…

We construct a two-dimensional bosonic symmetry-protected topological (SPT) paramagnet protected by an on-site $G=\mathbb{Z}_4^{\times 3}$ symmetry, starting from a three-component $\mathbb{Z}_4$ Potts paramagnet on a triangular lattice.…

Given a (genus 2) cube-with-holes M, i.e. the complement in S^3 of a handlebody H, we relate intrinsic properties of M (like its cut number) with extrinsic features depending on the way the handlebody H is knotted in S^3. Starting from a…

Graded skew-commutative rings occur often in practice. Here are two examples: 1) The cohomology ring of a compact three-dimensional manifold. 2) The cohomology ring of the complement of a hyperplane arrangement (the Orlik-Solomon algebra).…