Related papers: Counterexamples of the Geometrization Conjecture
In a paper of Bosio and Meersseman (Real quadrics in Cn, complex manifolds and convex polytopes) the following is conjectured: If P is dual neighborly, then Zp is diffeomorphic to the connected sum of products of spheres. In this paper a…
We construct an example of a closed manifold with a nonflat reducible locally metric connection such that it preserves a conformal structure and such that it is not the Levi-Civita connection of a Riemannian metric.
We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.
We study effective versions of unlikely intersections of images of torsion points of elliptic curves on the projective line.
The Isomorphism Conjectures are translated into the language of homotopical algebra, where they resemble Thomason's descent theorems.
Using the local bijectivity of Keller maps, we give a proof of two-dimensional Jacobian conjecture.
Let $E/\mathbb{Q}$ be an elliptic curve and $p > 2$ be a prime of good ordinary reduction for $E$. Assume that the residue representation associated with $(E, p)$ is irreducible. In this paper, we prove more cases on several Iwasawa main…
A minimal counterexample to the Erd\H{o}s-Gy\'arf\'as conjecture is a graph of minimum possible order and size with minimum degree at least 3 that contains no cycle whose length is a power of 2. Markstr\"om observed that any such graph must…
We show that if there exists a counter example for the rational case of the Franks-Misiurewicz conjecture, then it must exhibit unbounded deviations in the complementary direction of its rotation set.
We prove several extensions of the Erdos-Fuchs theorem.
This paper has been withdrawn by the author because Conjecture 1 is false. Please see arXiv:0901.2093 for a justification that Conjecture 1 is false. The other main results are also available from the above URL.
We consider here a generalization of a well known discrete dynamical system produced by the bisection of reflection angles that are constructed recursively between two lines in the Euclidean plane. It is shown that similar properties of…
In this article, we list a few hypergeometric supercongruence conjectures based on two evaluation formulas of Whipple and numeric data computed using Magma and Sagemath.
Using algebraic transformations and equivalent reformulations we derive a number of new results from some earlier ones (by the author) in more accepted terms closely related to well-known conjectures of Bondy and Jung including a number of…
Using geometric homology and cohomology we give a simple and conceptual proof of the Thom isomorphism theorem.
A ``self--similar'' example is constructed that shows that a conjecture of N. U. Arakelyan on the order of decrease of deficiencies of an entire function of finite order is not true.
We survey several results known on sampling in computational geometry.
In this paper we introduce elements of algebraic geometry over an arbitrary algebraic structure. We prove Unification Theorems which gather the description of coordinate algebras by several ways.
We answer a question that was asked by Albert Baernstein II, regarding the coefficients of circular symmetrization. The conjecture is not true generically.
In this article, we pursue the study begun in \cite{Lup02} on the cohomology of rationally elliptic coformal spaces. Consequently, we complete, for such spaces, the proof of Lupton's conjecture and deduce Hilali's.