arXiv research

Researchers found the smallest Laplace eigenvalue for homogeneous 3-spheres.

New $G_2$-instantons found on 3-sphere's spinor bundle.

We consider an embedding of a $2$-dimensional CW complex into the $3$-sphere, and construct it's dual graph. Then we obtain a homogeneous system of linear equations from the $2$-dimensional CW complex in the first homology group of the complement of the dual graph. By checking that the homogeneous system of linear equa…

Using the conformally invariant Cotton tensor, we define a geometric flow, the "Cotton flow", which is exclusive to three dimensions. This flow tends to evolve the initial metrics into conformally flat ones, and is somewhat orthogonal to the Yamabe flow, the latter being a flow within a conformal class. We define an en…

The goal of this paper is to establish the classification of all homogeneous surfaces of 3-sphere by using the moving frame method. We will show that such surfaces are 2-spheres and flat torus.

A new geometric flow $K$-flow on 3-manifolds shrinks or preserves homogeneous spheres.

The paper constructs scalar invariants for surfaces in a 3-sphere using Minkowski spacetime.

In this paper, we describe a new surprising example of a fibration of the Clifford torus S3 x S3 in the 7-sphere by great 3-spheres, which is fiberwise homogeneous but whose fibers are not parallel to one another. In particular it is not part of a Hopf fibration. A fibration is fiberwise homogeneous when for any two fi…

Study shows isospectral Dirac metrics on 3-spheres are isometric.

Researchers compute the spectrum of Hodge-Laplacian on 1-forms for SU(2) and SO(3).

Researchers identify only two types of tori with specific energy constraints.

Heinz Hopf's famous fibrations of the 2n+1-sphere by great circles, the 4n+3-sphere by great 3-spheres, and the 15-sphere by great 7-spheres have a number of interesting properties. Besides providing the first examples of homotopically nontrivial maps from one sphere to another sphere of lower dimension, they all share…

The paper describes a parametrisation of harmonic maps from a 2-torus to the 3-sphere.

In this paper we prove that a wild knot $K$ which is the limit set of a Kleinian group acting conformally on the unit 3-sphere, with its standard metric, is homogeneous: given two points $p, q\in{K}$ there exists a homeomorphism $f$ of the sphere such that $f(K)=K$ and $f(p)=q$. We also show that if the wild knot is a …

A fibration of a Riemannian manifold is fiberwise homogeneous if there are isometries of the manifold onto itself, taking any given fiber to any other one, and preserving fibers. Examples are fibrations of Euclidean n-space by parallel n-planes, and the Hopf fibrations of the round n-sphere by great n-spheres. In this …

Using basic homotopy constructions, we show that isomorphism classes of string structures on spin bundles are naturally given by certain degree 3 cohomology classes, which we call string classes, on the total space of the bundle. Using a Hodge isomorphism, we then show that the harmonic representative of a string class…

Study $SL(2,\mathbb{C})$ connections on Seifert-fibered spaces using gauge theory.

Study on 3-sphere Goeritz group's twisted first homology group.

This paper concerns the problem of existence of taut foliations among 3-manifolds. Since the contribution of David Gabai, we know that closed 3-manifolds with non-trivial second homology group admit a taut foliations. The essential part of this paper focuses on Seifert fibered homology 3-spheres. The result is quite di…

Study Ricci iteration on spheres and projective spaces, proving existence and convergence.

Stable 2-lobed Delaunay tori found in 3-sphere.

Characterizes a specific type of convex curves on a 3-sphere.

Real algebraic structures help classify overtwisted contact 3-spheres.

Disk complexes show 3-sphere surfaces are topologically minimal.

This paper shows how to unknot 2-manifolds in 3-sphere using twistings.

We show that a graph manifold which is a Z-homology 3-sphere not homeomorphic to either the 3-sphere or the Poincaré homology 3-sphere admits a horizontal foliation. This combines with known results to show that the conditions of not being an L-space, of having a left-orderable fundamental group, and of admitting a co-…

The paper examines conditions for contact surgeries on rational homology 3-spheres.

5 minimal tori found in 3-spheres with positive Ricci curvature.

For any knot, a 3-sphere triangulation exists with a knotted edge.

New algorithm for recognizing 3-spheres using Groebner basis methods.

New rational homology 3-spheres found that can't bound definite 4-manifolds.

Minimal surfaces in spheres found for any genus.

The paper studies invariants of surfaces in the 3-sphere using handlebody-links.

Paper finds infinitely many 3-spheres without nice orderings.

Flat tori in 3-sphere have π extrinsic diameter under specific conditions.

Classifies Legendrian Hopf links in 3-sphere.

Diagrammatic method characterizes non-split surfaces in 3-sphere.

The paper classifies decompositions of 3-sphere and lens spaces with handlebodies.

We prove Mayberry-Murasugi's formula for links in homology 3-spheres, which was proved before only for links in the 3-sphere. Our proof uses Franz-Reidemeister torsions.

Classifies SL(2;C) representations of a Brieskorn homology 3-sphere.

First examples of 3-spheres smoothly embedding in S^2 x S^2 but not S^4.

Study shows knots in 3-manifolds imply 3-sphere if certain conditions met.

Perelman's proof confirmed, new method uses 4D topology.

Study shows infinite order in mapping class groups for certain 3D shapes.

Reduces weak reducing pairs to spheres in 3-sphere Heegaard surfaces.

Constructs fat, shellable 3-spheres with specific $f$-vectors.

Study invariants of $\mathbb{Z}/p$-homology 3-spheres from abelianization of mapping class groups.

Researchers compute Reidemeister torsion for a specific 3-sphere.