Related papers: Homogeneous Transformation Groups of the Sphere
Based on Morse theory for the energy functional on path spaces we develop a deformation theory for mapping spaces of spheres into orthogonal groups. This is used to show that these mapping spaces are weakly homotopy equivalent, in a stable…
We characterize the cyclic branched covers of the 2-sphere where every homeomorphism of the sphere lifts to a homeomorphism of the covering surface. This answers a question that appeared in an early version of the erratum of Birman and…
It is shown that quantum homogeneous spaces of a quantum group H can be viewed as fibres of quantum fibrations with the total space H that are dual to coalgebra bundles. As concrete examples of such structures the fibrations with the…
We investigate analogues of some of the classical results in homogeneous dynamics in non-linear setting. Let $G$ be a closed subgroup of the group of automorphisms of a biregular tree and $\Gamma<G$ a discrete subgroup. For a large class of…
The primary algebraic model of a ring spectrum is the ring of homotopy groups. We introduce the secondary model which has the structure of a secondary analogue of a ring. This new algebraic model determines Massey products and cup-one…
We prove that every distortion element in the group of diffeomorphisms of the 2-sphere which has some recurrent point that is not fixed is an irrational pseudo-rotation. Moreover we prove that the differential of a distortion element in the…
In this survey, we present most recent highlights from the study of the homology cobordism group, with a particular emphasis on its long-standing and rich history in the context of smooth manifolds. Further, we list various results on its…
In this survey, we review how the global structure of the stable homotopy category gives rise to the chromatic filtration. We then discuss computational tools used in the study of local chromatic homotopy theory, leading up to recent…
We investigate several situations where the local homogeneity of a geometric structure on a dense open subset of a manifold implies the local homogeneity everywhere. This results in a strengthening of the conclusions in Gromov's open-dense…
We study the displacement function of homeomorphisms isotopic to the identity of the universal one-dimensional solenoid and we get a characterization of the lifting property for an open and dense subgroup of the isotopy component of the…
We survey recent work on the geometry and dynamics of transverse subgroups of semi-simple Lie groups.
A structure is called homogeneous if every isomorphism between finite substructures of the structure extends to an automorphism of the structure. Recently, P. J. Cameron and J. Ne\v{s}et\v{r}il introduced a relaxed version of homogeneity:…
We put in a general framework the situations in which a Riemannian manifold admits a family of compatible complex structures, including hyperkahler metrics and the Spin-rotations of arxiv:1302.2846. We determine the (polystable) holomorphic…
A structure is called homogeneous if every isomorphism between finitely induced substructures of the structure extends to an automorphism of the structure. Recently, P. J. Cameron and J. Ne\v{s}et\v{r}il introduced a relaxed version of…
Let $G$ be a complex connected reductive algebraic group and $G/B$ denote the flag variety of $G$. A $G$-homogeneous space $G/H$ is said to be {\it spherical} if $H$ acts on $G/B$ with finitely many orbits. A class of spherical homogeneous…
We present a way of constructing and deforming diffeomorphisms of manifolds endowed with a Lie group action. This is applied to the study of exotic diffeomorphisms and involutions of spheres and to the equivariant homotopy of Lie groups.
The set of all closed subgroups of a profinite carries a natural profinite topology. This space of subgroups can be classified up to homeomorphism in many cases, and tight bounds placed on its complexity as expressed by its scattered…
A simplified calculation of the structure constants of the diffeomorphism group of the two-sphere is presented
We prove that for finitely generated abelian groups $A$ and $B$, the space of $\mathbb{E}_\infty$-ring maps between the spherical groups rings $\mathbb{S}[A] \to \mathbb{S}[B]$ is equivalent to the discrete set of group homomorphisms $A \to…
The sets of closed and closed-normal subgroups of a profinite group carry a natural profinite topology. Through a combination of algebraic and topological methods the size of these subgroup spaces is calculated, and the spaces partially…