Related papers: On 4-dimensional smooth Poincare conjecture
We prove the Tate conjecture for integral degree 4 classes on a smooth cubic hypersurface X of dimension 4 over an algebraic closure of a field finitely generated over its prime subfield.
In this paper we provide a sharp characterization of the smooth four-dimensional sphere. The assumptions of the theorem are conformally invariant, and can be reduced to an L^2 inequality of the Weyl tensor and positivity of the Yamabe…
We prove a version of Poincar\'e's polyhedron theorem whose requirements are as local as possible. New techniques such as the use of discrete groupoids of isometries are introduced. The theorem may have a wide range of applications and can…
This note gives a new elementary proof of Poincar\'e-Miranda theorem based on Sard's theorem and the simple classification of one-dimensional manifolds.
We prove a Poincare type inequality for differential forms on compact manifolds by means of a constructive 'globalization' of a local Poincare inequality on convex sets.
In this paper, we proved the normal scalar curvature conjecture and the Bottcher-Wenzel conjecture.
A trisection of a smooth, closed, oriented 4-manifold is a decomposition into three 4-dimensional 1-handlebodies meeting pairwise in 3-dimensional 1-handlebodies, with triple intersection a closed surface. The fundamental groups of the…
We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.
This article is a first step in establishing a link between the Donaldson polynomials and Seiberg-Witten invariants of a smooth 4-manifold.
We outline a simple proof of PC without surgeries using the homogeneous flow introduced in [O].
We prove a four dimensional version of the Bernstein Theorem, with complex polynomials being replaced by quaternionic polynomials. We deduce from the theorem a quaternionic Bernstein's inequality and give a formulation of this last result…
There are many four vertex type theorems appearing in the literature, coming in both smooth and discrete flavors. The most familiar of these is the classical theorem in differential geometry, which states that the curvature function of a…
The aim of the work is to prove the following main theorem. Theorem. Let M3 be a three-dimensional, connected, simple-connected, closed, compact, smooth manifold. Tnen the manifold M3 is diffeomorphic to the three-dimensional sphere.
In this note we give a p-adic proof of Hodge symmetry for smooth, projective threefolds over complex numbers.
A classification theorem for 4-dimensional conformally flat QK3-manifolds is proved.
We offer an approach to the smooth 4-dimensional Schoenflies conjecture via pseudo-isotopy theory.
Motivated by the Poincare conjecture, we study properties of digital n-dimensional spheres and disks, which are digital models of their continuous counterparts. We introduce homeomorphic transformations of digital manifolds, which retain…
In this paper, we prove a conjecture of Schnell in the surface case.
This paper proves that any compact, closed, simply connected and connected three dimensional stellar manifold is stellar equivalent to the three dimensional sphere.
We prove the termination of 4-fold canonical flips.