Related papers: A homotopy-theoretic context for CKM/Birkhoff reno…

In this paper, we classify the homotopy types of the total spaces of $S^{2k-1}$-bundles (or fibrations) over $S^{2k}$ for $2\leq k\leq 6$. One of the two key new ingredients in the argument is the new necessary and sufficient conditions for…

We construct a rational homotopy-theoretic model for a classifying space of locally conformally symplectic structures on four-manifolds, and use it to definition a cobordism category of three-manifolds `anchored' by principal $\Omega^2 S^2$…

We give a systematic description of a canonical renormalisation procedure of stochastic PDEs containing nonlinearities involving generalised functions. This theory is based on the construction of a new class of regularity structures which…

We first want to consider the formal deformation of a fibered manifold $P \rightarrow M$ as a (bi-)module or subalgebra, where $M$ has a given differential star product. Consequently we want to find obstructions for the existence of a…

A geometric characterization of the structure of the group of automorphisms of an arbitrary Birkhoff-Grothendieck bundle splitting $\bigoplus_{i=1}^{r} \mathcal(m_{i})$ over $\mathbb{C}\mathbb{P}^{1}$ is provided, in terms of its action on…

Let $M$ be a closed 4-manifold with $\pi_2(M)\cong{Z}$. Then $M$ is homotopy equivalent to either $CP^2$, or the total space of an orbifold bundle with general fibre $S^2$ over a 2-orbifold $B$, or the total space of an $RP^2$-bundle over…

Let $M$ be a closed, oriented, simply connected 6-manifold. After localization away from 2, we give a homotopy decomposition of $\Sigma M$ in terms of spheres, Moore spaces and other recognizable spaces. As applications we calculate…

We describe a construction of Riemannian metrics of nonnegative sectional curvature on a closed smooth nonorientable 4-manifold with fundamental group of order two that realizes a homotopy class that was not previously known to contain…

In the present paper we consider a special class of locally trivial bundles with fiber a matrix algebra. On the set of such bundles over a finite $CW$-complex we define a relevant equivalence relation. The obtained stable theory gives us a…

We present an intrinsic geometric classification of the supermanifold of maps from $\mathbb{R}^{0|2}$ to any smooth manifold $S$, avoiding auxiliary structures. The key isomorphism relates this space to the pullback of the decomposable…

We present a construction of a canonical G_2 structure on the unit sphere tangent bundle S_M of any given orientable Riemannian 4-manifold M. Such structure is never geometric or 1-flat, but seems full of other possibilities. We start by…

Let $\pi: P\to B$ be a locally trivial fiber bundle over a connected CW complex $B$ with fiber equal to the closed symplectic manifold $(M,\om)$. Then $\pi$ is said to be a symplectic fiber bundle if its structural group is the group of…

This paper studies the (small) quantum homology and cohomology of fibrations $p: P\to S^2$ whose structural group is the group of Hamiltonian symplectomorphisms of the fiber $(M,\om)$. It gives a proof that the rational cohomology splits…

We define a class of symplectic fibrations called symplectic configurations. They are natural generalization of Hamiltonian fibrations. Their geometric and topological properties are investigated. We are mainly concentrated on integral…

In the present paper we study some homotopy invariants which can be defined by means of bundles with fiber a matrix algebra. We also introduce some generalization of the Brauer group in the topological context and show that any its element…

Given the Lagrangian fibration $T^4\to T^2$ and a Lagrangian submanifold, exhibiting an elliptic umbilic and supporting a flat line bundle, we study, in the context of mirror symmetry, the ``quantum'' corrections necessary to solve the…

We provide a unique normal form for rank two irregular connections on the Riemann sphere.In fact, we provide a birational model where we introduce apparent singular points and where the bundlehas a fixed Birkhoff-Grothendieck decomposition.…

We construct smooth bundles with base and fiber products of two spheres whose total spaces have non-vanishing $\hat{A}$-genus. We then use these bundles to locate non-trivial rational homotopy groups of spaces of Riemannian metrics with…

Let P be a principal bundle with semisimple compact simply connected structure group G over a compact simply connected four-manifold M. In this note we give explicit formulas for the rational homotopy groups and cohomology algebra of the…

The symplectomorphism group of a 2-dimensional surface is homotopy equivalent to the orbit of a filling system of curves. We give a generalization of this statement to dimension 4. The filling system of curves is replaced by a decomposition…