Related papers: Period three actions on the three-sphere

This paper gives the cohomology classification of finitistic spaces X equipped with free actions of the group G = S3 and the orbit space X/G is the integral or mod 2 cohomology quaternion projective space HPn. We have proved that X is the…

The aim of the work is to prove the following main theorem. Theorem. Let M3 be a three-dimensional, connected, simple-connected, closed, compact, smooth manifold. Tnen the manifold M3 is diffeomorphic to the three-dimensional sphere.

We show that, in the unit tangent bundle of a hyperbolic orbisphere with cone points of order 3, 3, 4, the lift of the shortest periodic geodesic is homeomorphic to the complement of the figure-eight knot in the 3-sphere. The proof…

A hyperbolic group acts by homeomorphisms on its Gromov boundary. We show that if this boundary is a topological n-sphere the action is topologically stable in the dynamical sense: any nearby action is semi-conjugate to the standard…

For n at least 3, let SAut(F_n) denote the unique subgroup of index two in the automorphism group of a free group. The standard linear action of SL(n,Z) on R^n induces non-trivial actions of SAut(F_n) on R^n and on S^{n-1}. We prove that…

We prove that every closed, connected contact 3-manifold can be obtained from the 3-sphere with its standard contact structure by contact surgery of coefficient plus or minus 1 along a Legendrian link. As a corollary, we derive a result of…

Let $M$ be a symplectic manifold, equipped with a Hamiltonian action of a torus $T$. We give an explicit formula for the rational cohomology ring of the symplectic quotient $M//T$ in terms of the cohomology ring of $M$ and fixed point data.…

Let $\Gamma$ be a group of type rotating automorphisms of a building $\fX$ of type $\tilde A_n$ and order $q$. Suppose that $\G$ acts freely and transitively on the vertex set of $\fX$. Then the action of $\Gamma$ on the boundary of $\fX$…

We consider surfaces of revolution in the three-dimensional Euclidean space which are of coordinate finite type with respect to the third fundamental form. We show that a surface of revolution satisfying the preceding relation is a catenoid…

The article provides proofs for the regularity of Dirac eigenfunctions, subject to MIT boundary conditions employed on various types of open sets ranging from smooth ones to convex polygons in two dimensions, as well as on half-space and…

We prove that for any knot $K$, there exists a one-vertex triangulation of the $3$-sphere containing an edge forming $K$. The proof is constructive, and based on fully augmented links. We use our method to produce ``complicated'' simplicial…

It is clear that every rational surgery on a Hopf link in $3$-sphere is a lens space surgery. In this note we give an explicit computation which lens space is a resulting manifold. The main tool we use is the calculus of continued…

We extend the Cahn-Landau-de Gennes mean field theory of binary mixtures to understand the wetting thermodynamics of a three phase system, that is in contact with an external surface which prefers one of the phases. We model the system…

We show that holomorphic riemannian metrics on compact complex threefolds are locally homogeneous (the pseudogroup of local isometries acts transitively on the manifold).

We classify polar isometric actions on simply connected 3-dimensional Riemannian homogeneous spaces, up to orbit equivalence. In particular, we classify extrinsically homogeneous surfaces in such spaces and study the geometry of the orbit…

In this paper we consider a free boundary problem in the 3-dimensional Lorentz-Minkowski space $\l^3$ which deals spacelike surfaces whose mean curvature is a linear function of the time coordinate and the boundary moves in a given support…

Let $X$ be a finite CW-complex having mod $p$ cohomology isomorphic to a wedge of three spheres $\mathbb{S}^n\vee \mathbb{S}^m \vee \mathbb{S}^l,~ 1\leq n \leq m \leq l$. The aim of this paper is to determine the fixed point sets of actions…

We prove that a closed, simply connected, positively curved, cohomogeneity-three manifold whose quotient space has no boundary is rationally elliptic, thus providing a generalization of similar results regarding rational ellipticity of…

We prove an existence and uniqueness theorem about spherical helicoidal (in particular, rotational) surfaces with prescribed mean or Gaussian curvature in terms of a continuous function depending on the distance to its axis. As an…

We study spectral action for Riemannian manifolds with boundary, and then generalize this to noncommutative spaces which are products of a Riemannian manifold times a finite space. We determine the boundary conditions consistent with the…