Related papers: Period three actions on the three-sphere
We establish lower bounds on the dimensions in which arithmetic groups with torsion can act on acyclic manifolds and homology spheres. The bounds rely on the existence of elementary p-groups in the groups concerned. In some cases, including…
An approach due to Wojtkovski [9], based on the Jacobi fields, is applied to study sets of 3-period orbits in billiards on hyperbolic plane and on two-dimensional sphere. It is found that the set of 3-period orbits in billiards on…
We show how the periodicity of a homology sphere is reflected in the Reshetikhin-Turaev-Witten invariants of the manifold. These yield a criterion for the periodicity of a homology sphere.
Locally standard $T$-pseudomanifolds were introduced by the authors in a previous work. They are topological stratified pseudomanifolds equipped with torus actions. Their equivariant homeomorphism types are classified by characteristic data…
The convex hull on three points in two dimensional euclidean space of three flat edges (trihedron) was studied. The Bohr-Sommerfeld quantization of the area of space is performed. It is shown that it reproduces exactly the equidistant…
We classify connected sums of three-dimensional lens spaces which smoothly bound rational homology balls. We use this result to determine the order of each lens space in the group of rational homology 3-spheres up to rational homology…
A necessary and sufficient algebraic condition for a diffeomorphism over a surface embedded in the 3-sphere to be induced by a regular homotopic deformation is discussed, and a formula for the number of signed pass moves needed for this…
By considering a spatial curve in a Euclidean space, we use its components, together with attaining a cyclic matrix, to show that this matrix is homothetic too and is in correspondence with a homothetic motion. Furthermore, if the curve…
We prove that every closed characteristic of minimal action on the boundary of a uniformly convex domain in $\R^4$ bounds a disk-like global surface of section. A corollary is that the cylindrical symplectic capacity of a convex body in…
In this paper, we consider decompositions of 3-manifolds with three handlebodies. We classify such decompositions of the 3-sphere and lens spaces with small genera. These decompositions admit operations called stabilizations. We also…
For an integral homology 3-sphere embedded asymptotically flatly in an Euclidean space, we find a natural framing extending the standard trivialization on the asymptotically flat part.
A free action of a finite group on an odd-dimensional sphere is said to be almost linear if the action restricted to each cyclic or 2-hyperelementary subgroup is conjugate to a free linear action. We begin this survey paper by reviewing the…
Using Freedman and Quinn's result for $\mathbb{Z}$-homology 3-spheres, we show that a 3-dimensional homology handle with trivial Alexander polynomial bounds a homology $S^1\times D^3$. As a consequence, a distinguished homology handle with…
We prove that under some assumptions on the mean curvature the set of umbilical points of an immersed surface in a $3$-dimensional space form has positive measure. In case of an immersed sphere our result can be seen as a generalization of…
We show that every continuous action of a finite group on a smooth three-manifold is a uniform limit of smooth actions.
In this paper we describe a procedure to simplify any given triangulation of the 3-sphere using Pachner moves. We obtain an explicit exponential-type bound on the number of Pachner moves needed for this process. This leads to a new…
We present results of numerical calculations showing a three-body orbit's period's $T$ dependence on its topology. This dependence is a simple linear one, when expressed in terms of appropriate variables, suggesting an exact mathematical…
Given a knot in a closed connected orientable 3-manifold we prove that if the exterior of the knot admits an aperiodic contact form that is Euclidean near the boundary, then the 3-manifold is diffeomorphic to the 3-sphere and the knot is…
Our main aim is to present a geometrically meaningful formula for the fundamental solutions to a second order sub-elliptic differential equation and to the heat equation associated with a sub-elliptic operator in the sub-Riemannian geometry…
We show that, for $\varepsilon=\dfrac{1}{4000}$, any action of a finite cyclic group by $(1+\varepsilon)$-bilipschitz homeomorphisms on a closed 3-manifold is conjugated to a smooth action.