Related papers: On the 3-Dimensional Poincar\'e Conjecture and the…
The aim of this article is to introduce invariants of oriented, smooth, closed four-manifolds, built using the Floer homology theories defined in two earlier papers (math.SG/0101206 and math.SG/0105202). This four-dimensional theory also…
We study a four-dimensional gauge theory of the Poincar\'e group with topological action which generalizes some well-known two-dimensional gravity models. We classify the spherically symmetric solutions and discuss the perturbative…
A non-algorithmic, generalized version of a recent result, asserting that a natural relaxation of the Koml\'os conjecture from boolean discrepancy to spherical discrepancy is true, is proved by a very short argument using convex geometry.
There has been substantial calculational progress in the last few years for gauge theory amplitudes which involve massless four dimensional particles. One of the central ingredients in this has been the ability to keep precise track of the…
In this thesis we take Einstein theory in dimension four seriously, and explore the special aspects of gravity in this number of dimension. Among the many surprising features in dimension four, one of them is the possibility of `Chiral…
In this paper we investigate the Erd\"os/Falconer distance conjecture for a natural class of sets statistically, though not necessarily arithmetically, similar to a lattice. We prove a good upper bound for spherical means that have been…
This is a first in a series of papers, devoted to the relation betwwen three-manifolds and number fields. The present paper studies first homology of finite coverings of a three-manifold with primary interest in the Thurston $b_1$…
We will simplify earlier proofs of Perelman's collapsing theorem for 3-manifolds given by Shioya-Yamaguchi and Morgan-Tian. Among other things, we use Perelman's critical point theory (e.g., multiple conic singularity theory and his…
We construct Schroedinger-like solutions of the Vasiliev higher spin theory in D>3 dimension. Symmetries of such solutions and the linearised equation of motion for the scalar on such backgrounds are analysed. We further propose Galilean…
In this note we gather and review some facts about existence of toric spaces over 3-dimensional simple polytopes. First, over every combinatorial 3-polytope there exists a quasitoric manifold. Second, there exist combinatorial 3-polytopes,…
We prove that semisimple 4-dimensional oriented topological field theories lead to stable diffeomorphism invariants and can therefore not distinguish homeomorphic closed oriented smooth 4-manifolds and homotopy equivalent simply connected…
We study a non-Riemannian modification of 5-dimensional Kaluza-Klein theory. In our proposal the Riemannian structure of the five-dimensional manifold is replaced by a Weyl-integrable one. In this context a 4-dimensional Poincar$\grave{e}$…
We prove the "Sullivan Conjecture" on the classification of 4-dimensional complete intersections up to diffeomorphism. Here an $n$-dimensional complete intersection is a smooth complex variety formed by the transverse intersection of $k$…
We study Poincar\'e Duality in the context of abstract 6-functor formalisms. In particular, we give a small and simple list of assumptions that implies Poincar\'e Duality. As an application, we give new uniform (and essentially formal)…
This paper is an expansion of my lecture for David Epstein's birthday, which traced a logical progression from ideas of Euclid on subdividing polygons to some recent research on invariants of hyperbolic 3-manifolds. This `logical…
The purpose of this short note is to relate a representation formula due to the Author and P. Romon for Lagrangian surfaces (see math.DG/0009202) to a more general Weierstrass representation type formula found by Konopelchenko for surfaces…
Based on the gauge semi-simple tensor extension of the Poincar\'e group another alternative approach to the cosmological term problem is proposed.
Two conjectures relating the Kodaira dimension of a smooth projective variety and existence of number of nowhere vanishing 1-forms on the variety are proposed and verified in dimension 3.
A "Two-Spaceship Paradox" in special relativity is resolved and discussed. We demonstrate a nonstandard resolution to the "two-spaceship paradox" by explicit calculation using Generalized Principle of limiting 4-dimensional symmetry…
It is well-known that the first and second Painlev\'e equations admit solutions characterised by divergent asymptotic expansions near infinity in specified sectors of the complex plane. Such solutions are pole-free in these sectors and…