Related papers: Homogeneous Hypercomplex Structures II - Coset Spa…

We study the rational homotopy types of classifying spaces of automorphism groups of smooth simply connected manifolds of dimension at least five. We give dg Lie algebra models for the homotopy automorphisms and the block diffeomorphisms of…

$p$-Adic compactifications of geometric loop and diffeomorphism groups of compact manifolds on finite-dimensional spaces over non-Archimedean fields are investigated. Weakened topology is introduced. The structure of newly constructed…

We provide a complete classification of the possible cofinal structures of the families of precompact (totally bounded) sets in general metric spaces, and compact sets in general complete metric spaces. Using this classification, we…

We describe a geometric compactification of the moduli stack of left invariant complex structures on a fixed real Lie group or a fixed quotient. The extra points are CR structures transverse to a real foliation.

We survey some recent advances in the homotopy theory of classifying spaces, and homotopical group theory. We focus on the classification of p-compact groups in terms of root data over the p-adic integers, and discuss some of its…

In math.SG/0303255, we discussed the connected components of the space of surface group representations for any compact connected semisimple Lie group and any closed compact (orientable or nonorientable) surface. In this sequel, we…

In this paper we consider the classification of minimal cellular structures of spaces of topological complexity two under some hypotheses on there graded cohomological algebra. This continues the method used by M.Grant et al. in [1].

We develop a general structure theory for compact homogeneous Riemannian manifolds in relation to the co-index of symmetry. We will then use these results to classify irreducible, simply connected, compact homogeneous Riemannian manifolds…

In this paper, we consider a simple class of stratified spaces -- 2-complexes. We present an algorithm that learns the abstract structure of an embedded 2-complex from a point cloud sampled from it. We use tools and inspiration from…

We present a new simple proof of the fact that certain group manifolds as well as certain homogeneous spaces G/H of dimension 4n admit a quaternionic triple of integrable complex structures that are covariantly constant with respect to the…

This is the second paper of a series dedicated to the study of Poisson structures of compact types (PMCTs). In this paper, we focus on regular PMCTs, exhibiting a rich transverse geometry. We show that their leaf spaces are integral affine…

We show that any homomorphism from the homeomorphism group of a compact 2-manifold, with the compact-open topology, or equivalently, with the topology of uniform convergence, into a separable topological group is automatically continuous.

We study groups of homeomorphic bijections on spaces that are finite unions of compact connected linearly ordered subsets. We prove that all such groups when endowed with the topology of point-wise convergence are topological groups. }

We prove that numerous negatively curved simply connected locally compact polyhedral complexes, admitting a discrete cocompact group of automorphisms, have automorphism groups which are locally compact, uncountable, non linear and virtually…

We consider locally homogeneous $CR$ manifolds and show that, under a condition only depending on their underlying contact structure, their $CR$ automorphisms form a finite dimensional Lie group.

In these notes we study left-invariant involutive structures on $\mathrm{SU}(2)$, the most na\"ive non-commutative compact Lie group. We determine closedness of the range (in the smooth topology) of a single complex vector field spanning…

Let $G$ be a Lie group with a biinvariant metric, not necessarily positive definite. It is shown that a certain construction carried out in an earlier paper for the fundamental group of a closed surface may be extended to an arbitrary…

We survey different tools to classify representations of compact Lie groups according to their cohomogeneity and apply these methods to the case of irreducible representations of cohomogeneity 6, 7 and 8.

We study spin structures on compact simply-connected homogeneous pseudo-Riemannian manifolds (M = G/H, g) of a compact semisimple Lie group G. We classify flag manifolds F = G/H of a compact simple Lie group which are spin. This yields also…

We show that contact reductions can be described in terms of symplectic reductions in the traditional Marsden-Weinstein-Meyer as well as the constant rank picture. The point is that we view contact structures as particular (homogeneous)…