Three-dimensional compact manifolds and the Poincare conjecture

TL;DR

This paper proves that any three-dimensional, simply connected, closed, smooth manifold is diffeomorphic to the three-dimensional sphere, confirming the Poincaré conjecture.

Contribution

It provides a proof of the Poincaré conjecture for three-dimensional manifolds, establishing a fundamental topological classification.

Findings

All simply connected, closed 3-manifolds are 3-spheres.

The theorem confirms the Poincaré conjecture.

The proof advances understanding of 3-manifold topology.

Abstract

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.