Related papers: Non-linear proper Fredholm maps and the stable hom…

In this paper we work in o-minimal structures with definable Skolem functions and show that a continuous definable map between Hausdorff locally definably compact definable spaces is definably proper if and only if it is proper morphism in…

The past years have seen rapid progress in the classification of topological materials. These diagnostical methods are increasingly getting explored in the pertinent context of magnetic structures. We report on a general class of electronic…

$\infty$-Harmonic maps are a generalization of $\infty$-harmonic functions. They can be viewed as the limiting cases of p-harmonic maps as p goes to infinity. In this paper, we give complete classifications of linear and quadratic…

We introduce the (general) homotopy groups of spheres as link invariants for Brunnian-type links through the investigations on the intersection subgroup of the normal closures of the meridians of strongly nonsplittable links. The homotopy…

Based on Morse theory for the energy functional on path spaces we develop a deformation theory for mapping spaces of spheres into orthogonal groups. This is used to show that these mapping spaces are weakly homotopy equivalent, in a stable…

We discuss the current state of knowledge of stable homotopy groups of spheres. We describe a new computational method that yields a streamlined computation of the first 61 stable homotopy groups, and gives new information about the stable…

In this paper we analyze some relationships between the topological complexity of a space $X$ and the category of $C_{\Delta_X},$ the homotopy cofibre of the diagonal map $\Delta_X:X\rightarrow X\times X.$ We establish the equality of the…

J.H.C. Whitehead defined a map $J_r:\pi_r(SO)\rightarrow \pi_r^s$ from the homotopy of the special orthogonal group to the stable homotopy of spheres. Within a toy model we show how the known computation for kernel$(J)$ leads to nonlinear…

The Reeb space of a continuous map is the space of all (elements representing) connected components of preimages endowed with the quotient topology induced from the natural equivalence relation on the domain. These objects are strong tools…

This work explores new classes of nonstationary stochastic sequences associated with polynomial hypergroups. Their covariance structures are analyzed through positive definite kernels and corresponding Hilbert spaces. Novel consistent…

We describe work on solutions of certain non-divergence type and therefore non-variational elliptic and parabolic systems on manifolds. These systems include Hermitian and affine harmonics which should become useful tools for studying…

The James fibrations give rise to the geometric EHP sequences of homotopy groups of spheres. Using techniques from the Lambda algebra, \cite{BCKQRS66} shows that there are similar long exact sequences of Ext groups defining the $E_{2}-$page…

We give a new proof of Faran's and Lebl's results by means of a new CR-geometric approach and classify all holomorphic mappings from the sphere in $\mathbb C^2$ to Levi-nondegenerate hyperquadrics in $\mathbb C^3$. We use the tools…

We formulate and prove a new variant of the Segal Conjecture describing the group of homotopy classes of stable maps from the p-completed classifying space of a finite group G to the classifying space of a compact Lie group K as the p-adic…

Let $N$ and $P$ be smooth closed manifolds of dimensions $n$ and $p$ respectively. Given a Thom-Boardman symbol $I$, a smooth map $f:N\to P$ is called an $\Omega^{I}$-regular map if and only if the Thom-Boardman symbol of each singular…

We prove the regularity of weak 1/2-harmonic maps from the real line into a sphere. The key point in our result is first a formulation of the 1/2-harmonic map equation in the form of a non-local linear Schr\"odinger type equation with a…

We study biharmonic maps and f-biharmonic maps from a round sphere $(S^2, g_0)$, the latter maps are equivalent to biharmonic maps from Riemann spheres $(S^2, f^{-1}g_0)$. We proved that for rotationally symmetric maps between rotationally…

In this note we give an algorithm to determine the rational homotopy type of the free and pointed mapping spaces $ map(F(\mathbb R^m,k), S^n)$ and $ map^*(F(\mathbb R^m,k), S^n)$. An explicit description of these spaces is given for $k=3$.…

The level spacing distributions in the Gaussian Unitary Ensemble, both in the ``bulk of the spectrum,'' given by the Fredholm determinant of the operator with the sine kernel ${\sin \pi(x-y) \over \pi(x-y)}$ and on the ``edge of the…

The space $\mathbf{H}^{4,2}$ of vectors of norm -1 in $\mathbb{R}^{4,3}$ has a natural pseudo-Riemannian metric and a compatible almost complex structure. The group of automorphisms of both of these structures is the split real form $G_2'$.…