Related papers: A parametrized version of the Borsuk Ulam theorem
The Wadge hierarchy was originally defined and studied only in the Baire space (and some other zero-dimensional spaces). We extend it here to arbitrary topological spaces by providing a set-theoretic definition of all its levels. We show…
This note studies the Burnside problem for homeomorphism groups of compact connected manifolds. For surfaces, we prove that the identity component of the homeomorphism group is torsion-free precisely when the surface is not the sphere,…
In this paper, we use new results together with established facts about Thurston's compactification of Teichm\"uller space to address the geometric P=W conjecture for $\mathrm{SL}(2,\mathbb{C})$, which concerns projective compactifications…
We study the Hamiltonian formulation for a parametrized electromagnetic field with the purpose of clarifying the interplay between parametrization and gauge symmetries. We use a geometric approach which is tailor-made for theories where…
Maps on a parameter space for expressing distribution functions are exactly derived from the Perron-Frobenius equations for a generalized Boole transform family. Here the generalized Boole transform family is a one-parameter family of maps…
Using the Abstract Cauchy-Kowalewski Theorem we prove that the $b$-family equation admits, locally in time, a unique analytic solution. Moreover, if the initial data is real analytic and it belongs to $H^s$ with $s > 3/2$, and the momentum…
We are motivated by a conjecture of A. and S. Katok to study the smooth cohomologies of a family of Weyl chamber flows. The conjecture is a natural generalization of the Livshitz Theorem to Anosov actions by higher-rank abelian groups; it…
In view of the complexity of the dynamics of learning in games, we seek to decompose a game into simpler components where the dynamics' long-run behavior is well understood. A natural starting point for this is Helmholtz's theorem, which…
We identify new families of duality-invariant theories of electrodynamics. We achieve this in two different ways. On the one hand, we present an algorithm to construct a one-parameter family of exactly duality-invariant theories from a…
This article derives closed-form parametric formulas for the Minkowski sums of convex bodies in d-dimensional Euclidean space with boundaries that are smooth and have all positive sectional curvatures at every point. Under these conditions,…
For W a finite Coxeter group, a formula is found for the size of W equivalence classes of subsets of a base. The proof is a case-by-case analysis using results and tables of Carter and Orlik/Solomon. As a corollary we obtain an alternating…
In this paper we consider several generalizations of the Borsuk-Ulam theorem for G-spaces and apply these results to Tucker type lemmas for G-simplicial complexes and PL-manifolds.
Motivated by Sarnak's conjecture on M\"obius orthogonality, we investigate the general problem of orthogonality for a bounded sequence to topological models of characteristic classes of measure-preserving automorphisms. Our main observation…
Given an Euclidean space, this paper elucidates the topological link between the partial derivatives of the Minkowski functional associated to a set (assumed to be compact, convex, with a differentiable boundary and a non-empty interior)…
In this work we prove the fact that, for a short time, it is possible to construct a smooth parametrized family of isometric embeddings of an arbitrary smooth parametrized family of Riemannian metrics on a smooth closed manifold into an…
We construct an example announced in the title. It answers in a strong way a well-known open problem in topological dynamics. In fact our construction is an existence theorem. It is based on a Borsuk-Ulam type theorem whose proof heavily…
The present work studies the robustness of certain basic homoclinic motions in an equilateral restricted four body problem. The problem can be viewed as a two parameter family of conservative autonomous vector fields. The main tools are…
The paper deals with the program of determining the complexity of various homeomorphism relations. The homeomorphism relation on compact Polish spaces is known to be reducible to an orbit equivalence relation of a continuous Polish group…
A real algebraic variety W of dimension m is said to be uniformly rational if each of its points has a Zariski open neighborhood which is biregularly isomorphic to a Zariski open subset of R^m. Let l be any nonnegative integer. We prove…
We use the Wa\'zewski topological principle to establish a number of new sufficient conditions for the existence of proper (defined on the entire time axis) solutions of essentially nonlinear nonautonomous systems. The systems under…