Related papers: Variations on a conjecture of Halperin
We prove some estimates on the spectrum of the Laplacian of the total space of a Riemannian submersion in terms of the spectrum of the Laplacian of the base and the geometry of the fibers. When the fibers of the submersions are compact and…
Let f:E-->B be a fibration of fiber F. Eilenberg and Moore have proved that there is a natural isomorphism of vector spaces between H^*(F;F_p) and Tor^{C^*(B)}(C^*(E),F_p). Generalizing the rational case proved by Sullivan, Anick [Hopf…
The Hilali Conjecture predicts that for a simply-connected elliptic space, the total dimension of the rational homotopy does not exceed that of the rational homology. Here we give a proof of this conjecture for a class of elliptic spaces…
Let k be an algebraically closed subfield of the complex numbers, and X a variety defined over k. One version of the Beilinson-Hodge conjecture that seems to survive scrutiny is the statement that the Betti cycle class map cl_{r,m} :…
Suppose a sequence $M_j$ of Alexandrov spaces collapses to a space $X$ with only weak singularities. Yamaguchi constructed a map $f_j:M_j\to X$ called an almost Lipschitz submersion for large $j$. We prove that if $M_j$ has a uniform…
We study a natural birational invariant for varieties over finite fields and show that its vanishing on projective space is equivalent to the Tate conjecture, the Beilinson conjecture, and the Grothendieck--Serre semi-simplicity conjecture…
We study fibred spaces with fibres in a structure category $\V$ and we show that cellular approximation, Blakers--Massey theorem, Whitehead theorems, obstruction theory, Hurewicz homomorphism, Wall finiteness obstruction, and Whitehead…
Pour tout $t\in\mN$ nous d\'efinissons un certain entier positif $\N_t$ et nous conjecturons: si $H$ est un fibr\'e de Gauss-Manin d'une fibration semi-stable alors la $t$-\`eme classe de Chern de $H$ est annul\'ee par $\N_t$. Nous…
We observe that the notion of a trivial Serre fibration, a Serre fibration, and being contractible, for finite CW complexes, can be defined in terms of the Quillen lifting property with respect to a single map M-->/\ of finite topological…
We prove that the weak Hilbert property ascends along a morphism of varieties over an arbitrary field of characteristic zero, under suitable assumptions.
It was proved by H. Whitney in 1933 that a Serre fibration of compact metric spaces admits a global section provided every fiber is homeomorphic to the unit interval [0,1]. An extension of the Whitney's theorem to the case when all fibers…
It was proved by H. Whitney in 1933 that a Serre fibration of compact metric spaces admits a global section provided every fiber is homeomorphic to the unit interval [0,1]. Results of this paper extend Whitney theorem to the case when all…
Let p be a fibration over a finite simplicial complex, whose fibers have the homotopy type of finite simplicial complexes. Then p is equivalent to an approximate fibration whose total space is a compact ENR. The proof uses homotopy coherent…
We generalize a result of Serre's to show that if every vertex of some fixed type of a convex subcomplex of an irreducible spherical building has an opposite, then the subcomplex is completely reducible.
The Chen-Ng\^o Conjecture predicts that the Hitchin morphism from the moduli stack of $G$-Higgs bundles on a smooth projective variety surjects onto the space of spectral data. The conjecture is known to hold for the group $GL_n$ and any…
We present a reduction of the Hilbert-Smith conjecture in the case of the finite dimensional orbit space to some algebraic topology problems.
The modularity of an elliptic curve $E/\mathbb Q$ can be expressed either as an analytic statement that the $L$-function is the Mellin transform of a modular form, or as a geometric statement that $E$ is a quotient of a modular curve…
Let K be a local field of mixte characteristics. We assume that the residue field is perfect. Let X\_K be a proper smooth scheme over K admitting an integer model X which is proper and semi-stable. In this article, we prove a period…
We provide new conditions under which the alternating projection sequence converges in norm for the convex feasibility problem where a linear subspace with finite codimension $N\geq 2$ and a lattice cone in a Hilbert space are considered.…
We give a short, simple and conceptual proof, based on spin structures, of sphere eversion: an embedded 2-sphere in $R^3$ can be turned inside out by regular homotopy. Ingredients of this eversion are seamlessly connected. We also give the…