Another way of answering Henri Poincare's fundamental question

TL;DR

This paper presents a novel approach to Poincare's fundamental question by constructing a homotopy disc from a simply connected 3-manifold, demonstrating it can be embedded into R^3, and thus proving the manifold is a sphere.

Contribution

It introduces a new method for proving a simply connected 3-manifold is a sphere by constructing an embeddable homotopy disc using stratification techniques.

Findings

Constructed a homotopy disc from a simply connected 3-manifold.

Demonstrated the homotopy disc can be embedded into R^3.

Proved the original manifold is topologically a sphere.

Abstract

After G. Perelman's solution of the Poincare Conjecture, this is a different way toward it. Given a simply connected, closed 3-manifold M, we produce a homotopy disc H, which arises from M by a finite sequence of simple modifications and, almost miraculously, can be imbedded into the ordinary space R^3. It follows that H is a disc, hence M is a sphere. In order to construct H, we use a special stratification of M, based on the fact that M is simply connected.