Related papers: Decompositions involving Anick's spaces
We study geometrical aspects of the space of fibrations between two given manifolds M and B, from the point of view of Frechet geometry. As a first result, we show that any connected component of this space is the base space of a…
This work is the geometric part of our proof of the weighted fundamental lemma, which is an extension of Ng\^o Bao Ch\^au's proof of the Langlands-Shelstad fundamental lemma. Ng\^o's approach is based on a study of the elliptic part of the…
In this paper we study the $p$-adic analytic geometry of the basic unitary group Rapoport-Zink spaces $\M_K$ with signature $(1,n-1)$. Using the theory of Harder-Narasimhan filtration of finite flat groups developed by Fargues in…
We study the general fibre of a formal deformation over the formal disk of a projective variety from the view point of abelian and derived categories. The abelian category of coherent sheaves of the general fibre is constructed directly…
Spacetime is represented by ordered sequences of topologically closed Poincare sections of the primary space constructed of primary empty cells. These mappings are constrained to provide homeomorphic structures serving as frames of…
A metric space $M$ us said to have the fibered approximation property in dimension $n$ (br., $M\in \mathrm{FAP}(n)$) if for any $\epsilon>0$, $m\geq 0$ and any map $g: I^m\times I^n\to M$ there exists a map $g':I^m\times I^n\to M$ such that…
Since the seminal work of Ambrosetti and Prodi, the study of global folds was enriched by geometric concepts and extensions accomodating new examples. We present the advantages of considering fibers, a construction dating to Berger and…
We study affine maps between affine manifolds. Even when the fibers are compact and diffeomorphic, two of them can inherit different affine structures from the source space. This leads to a fixed linear holonomy deformation theory of the…
Given a fibration over the circle, we relate the eigenspace decomposition of the algebraic monodromy, the homological finiteness properties of the fiber, and the formality properties of the total space. In the process, we prove a more…
I begin by explaining how Riemannian geometry can be understood in terms of principal fibre bundles and connections thereon. I then introduce and motivate the definition of a spinor structure in terms of familiar geometrical ideas. The…
Fiber-reinforcement is a universal feature of many biological tissues. It involves the interplay between fiber stiffness, fiber orientation, and the elastic properties of the matrix, influencing pattern formation and evolution in layered…
In this survey, we remind some fibrations structure theorems (also called Milnor's fibrations) recently proved in the real and complex case, in the local and global settings. We give several Poincar\'e-Hopf type formulae which relates the…
We prove the well-definedness of some deformations of the fibred biset category in characteristic zero. The method is to realize the fibred biset category and the deformations as the invariant parts of some categories whose compositions are…
We study the existence and properties of birationally equivalent models for elliptically fibered varieties. In particular these have either the structure of Mori fiber spaces or, assuming some standard conjectures, minimal models with a…
This text describes the fiber bundle structure and shows its universality for writing the laws of classical physics: newtonian, relativistic and quantum mechanics.
In the present paper we consider fibrations $f: S \ra B$ of an algebraic surface onto a curve $B$, with general fibre a curve of genus $g$. Our main results are: 1) A structure theorem for such fibrations in the case $g=2$ 2) A structure…
We describe pairs (p,n) such that n-dimensional affine space is fibered by pairwise skew p-dimensional affine subspaces. The problem is closely related with the theorem of Adams on vector fields on spheres and the Hurwitz-Radon theory of…
In this paper we study two types of fibrations associated with a 3-dimensional unital associative irreducible algebra and their basic properties. We investigate trivial principal fibrations of degenerate semi-Euclidean sphere and their…
In this paper, we consider certain topological properties along with certain types of mappings on these spaces defined by the notion of ideal convergence. In order to do that, we primarily follow in the footsteps of the earlier studies of…
Decomposition systems with rapidly decaying elements (needlets) based on Hermite functions are introduced and explored. It is proved that the Triebel-Lizorkin and Besov spaces on $\R^d$ induced by Hermite expansions can be characterized in…