Related papers: On Mimura's extension problem

We generalize the classical construction principles of infinite-dimensional real (and complex) Lie groups to the case of Lie groups over non-discrete topological fields. In particular, we discuss linear Lie groups, mapping groups, test…

We show how one can associate to a given class of finite type G-structures a classifying Lie algebroid. The corresponding Lie groupoid gives models for the different geometries that one can find in the class, and encodes also the different…

Hilbert--Lie groups are Lie groups whose Lie algebra is a real Hilbert space whose scalar product is invariant under the adjoint action. These infinite-dimensional Lie groups are the closest relatives to compact Lie groups. Here we study…

These notes have been prepared for the Workshop on "(Non)-existence of complex structures on $\mathbb{S}^6$", to be celebrated in Marburg in March, 2017. The material is not intended to be original. It contains a survey about the smallest…

This paper is on the connecting homomorphism in the long exact homotopy sequence of the evaluation fibration $ev_{p_0}:C(P,K)^K \to K$, where $C(P,K)^K \cong Gau(P)$ is the gauge group of a continuous principal $K$-bundle $P$ over a closed…

A discrete group which admits a faithful, finite dimensional, linear representation over a field $\mathbb F$ of characteristic zero is called linear. This note combines the natural structure of semi-direct products with work of A. Lubotzky…

Let $G_{2}$ be a group which acts trivially on an abelian group $G_{1}$. As is well known, each perturbed direct product of $G_{1}$ and $G_{2}$ under a 2-cocycle $\varepsilon\in Z^{2}(G_{2},G_{1})$ determines a central extension of $G_{1}$…

Desuspension Theorem for the steam $\Pi_{2^l-2}$ in stable homotopy groups of spheres is formulated and is proved. The proof is a minor revision of a theorem in the preprint \cite{A1} by the author (2010).

The classifying space BG of a topological group $G$ can be filtered by a sequence of subspaces $B(q,G)$, using the descending central series of free groups. If $G$ is finite, describing them as homotopy colimits is convenient when applying…

For any finite group G, we show that the 2-local G-equivariant stable homotopy category, indexed on a complete G-universe, has a unique equivariant model in the sense of Quillen model categories. This means that the suspension functor,…

We prove the symmetrising trace conjecture of Brou\'e, Malle and Michel for the generic Hecke algebra associated to the exceptional irreducible complex reflection group $G_{13}$. Our result completes the proof of the conjecture for the…

We find new conditions that the existence of nullity of the curvature tensor of an irreducible homogeneous space $M=G/H$ imposes on the Lie algebra $\mathfrak g$ of $G$ and on the Lie algebra $\tilde{\mathfrak g}$ of the full isometry group…

Groups $\Pi_k(X;\sigma)$ of "flagged homotopies" are introduced of which the usual (abelian for $k>1$) homotopy groups $\pi_k(X;p)$ is the limit case for flags $\sigma$ contracted to a point $p$. Calculus of exterior forms with values in…

We study the structure of a series of groups $\Gamma_n^4$ defined by Kim and Manturov. We show that the groups are finite for all $n \ge 6$ and in fact they are 2-step nilpotent $2$-groups.

Lie groupoids generalize transformation groups, and so provide a natural language for studying orbifolds and other noncommutative geometries. In this paper, we investigate a connection between orbifolds and equivariant stable homotopy…

Lie-Yamaguti algebras (or generalized Lie triple systems) are binary-ternary algebras intimately related to reductive homogeneous spaces. The Lie-Yamaguti algebras which are irreducible as modules over their inner derivation algebras are…

The second relative homotopy group \pi_2(V(\C),V(\R)) (of the complex relative to the real points of an algebraic variety) encodes interesting information about the `bubbling' phenomena of quantum cohomology. We consider these groups in…

We discuss the existence of Gribov ambiguities in $SU(m)\times U(1)$ gauge theories over the $n-$spheres. We achieve our goal by showing that there is exactly one conjugacy class of groups of gauge transformations for the theories given…

It was proven by Hitchin that any solution of his evolution equations for a half-flat SU(3)-structure on a compact six-manifold M defines an extension of M to a seven-manifold with holonomy in G_2. We give a new proof, which does not…

The content of this paper has no mathematical flaw except that the proof of the main theorem relies on the homotopy invariance of spectral invariants of topological Hamiltonian paths. Since the latter is still up in the air, the main result…