arXiv research

3-manifolds with two abelian-filled spaces.

Embeds 3-manifolds in symplectic 4-manifolds with constraints.

Embeds 3-manifolds into higher dimensions using open books.

Survey article on multibranched surfaces in 3-manifolds.

Study on embedding surfaces into 3-manifolds, focusing on equivariant cases.

Survey on embedding 3-manifolds in definite 4-manifolds, focusing on Donaldson's theorem.

Embeds complex 3-manifolds into symplectic space.

Smoothly embed 3-manifolds in 5-manifolds, simplifying topological to smooth.

The paper proves smooth minimal surfaces in hyperbolic 3-manifolds.

Study of codimension-1 embeddings in 3-manifolds using twist maps and push maps.

Study embeddings of 3-manifolds in $S^4$ with nilpotent fundamental groups.

The study explores symmetries of graphs in 3-manifolds and their induced homeomorphisms.

Study of pseudoconvex 3-manifolds in complex surfaces.

In this survey article we describe different ways of embedding fillings of contact 3-manifolds into closed symplectic 4-manifolds.

Geodesic surfaces embed into hyperbolic 3-manifolds for all finite group actions.

Embedding $3$-manifolds in $\mathbb{R}^4$ is obstructed by Heegaard curve complexes.

Study of 3-manifolds in 5-sphere using bridge decompositions.

The study explores how 3-manifolds embed locally flatly in $S^4$.

The study finds minimal volume hyperbolic 4-manifolds with embedded 3-manifolds.

New theorem shows embedding impossibility for certain 3-manifolds.

3-manifolds can be embedded almost in the spine of a trisected 4-manifold.

New families of embeddings in 4-manifolds, topologically trivial but smoothly non-trivial.

Study the embedding space of a Hopf link in 3D and 3-manifolds.

We consider embeddings of 3-manifolds in $S^4$ such that each of the two complementary regions has an abelian fundamental group. In particular, we show that an homology handle $M$ has such an embedding if and only if $π_1(M)'$ is perfect, and that the embedding is then essentially unique.

Counterexample disproves conjecture about 3-manifolds.

We prove that if S is a properly embedded incompressible surface in a compact 3-manifold M, then the fundamental group of S is separable in the fundamental group of M.

2-width of 3-manifolds is bounded by 2 but embeddings can have infinite 2-width.

Engel structures on bundles over 3-manifolds in complex 3-space.

The study provides a structure theorem for a new class of noncompact 3-manifolds.

This is a collection of notes on embedding problems for 3-manifolds. The main question explored is `which 3-manifolds embed smoothly in the 4-sphere?' The terrain of exploration is the Burton/Martelli/Matveev/Petronio census of triangulated prime closed 3-manifolds built from 11 or less tetrahedra. There are 13766 mani…

The paper introduces the spirality character of the almost fiber part for a closed essentially immersed subsurface of a closed orientable aspherical 3-manifold, which generalizes an invariant due to Rubinstein and Wang. The subsurface is virtually embedded if and only if the almost fiber part is aspiral, and in this ca…

New findings show some hyperbolic 3-manifolds can't be geometrically bounded.

We prove there exists a compact embedded minimal surface in a complete finite volume hyperbolic $3$-manifold $\mathcal{N}$. We also obtain a least area, incompressible, properly embedded, finite topology, $2$-sided surface. We prove a properly embedded minimal surface of bounded curvature has finite topology. This dete…

Paper proves existence of minimal surfaces in hyperbolic 3-manifolds.

An invariant of orientable 3-manifolds is defined by taking the minimum $n$ such that a given 3-manifold embeds in the connected sum of $n$ copies of $S^2 \times S^2$, and we call this $n$ the embedding number of the 3-manifold. We give some general properties of this invariant, and make calculations for families of le…

Enhances Hantzsche's theorem for 3-manifolds in 4D.

Totally umbilic surfaces in hyperbolic 3-manifolds are constructed and characterized.

We show that a smooth embedding of a closed 3-manifold in S^3 x R can be isotoped so that every generic level divides S^3 x t into two handlebodies (i.e., is Heegaard) provided the original embedding has a unique local maximum with respect to the R coordinate. This allows uniqueness of embeddings to be studied via the …

We prove existence of thick geodesic triangulations of hyperbolic 3-manifolds and use this to prove existence of universal bounds on the principal curvatures of surfaces embedded in hyperbolic 3-manifolds.

Given a sequence of properly embedded minimal surfaces in a $3$-manifold with local bounds on area and genus, we prove subsequential convergence, smooth away from a discrete set, to a smooth embedded limit surface, possibly with multiplicity, and we analyze what happens when one blows up the surfaces near a point where…

Embeddings of 3-manifolds into complex 3-space with specific tangents.

Study shows 3D shapes can't fit in certain 4D spaces.

In this paper we study embeddings of contact manifolds using braidings of one manifold about another. In particular we show how to embed many contact 3-manifolds into the standard contact 5-sphere. We also show how to obstruct braidings of one manifold about another using contact geometry.

Polynomials derived from Heegaard diagrams for 3-manifolds.

The study finds totally geodesic surfaces in hyperbolic 3-manifolds and verifies a conjecture.

Groups can embed uniformly but not act properly on contractible manifolds.

This paper is the fourth in a series where we describe the space of all embedded minimal surfaces of fixed genus in a fixed (but arbitrary) closed 3-manifold. The key is to understand the structure of an embedded minimal disk in a ball in $\RR^3$. This was undertaken in [CM3], [CM4] and the global version of it will be…

Study shows certain 4D hyperbolic links don't contain geodesic 3-manifolds.