The topological proof of the Poincare conjecture

TL;DR

This paper provides a topological proof of the Poincare conjecture by analyzing manifold crushing operations and their effects on simply-connectedness, splitting the problem into two key propositions and proving them.

Contribution

It introduces a novel topological approach to the Poincare conjecture by decomposing it into two manageable problems and proving their validity.

Findings

The operation preserves simply-connectedness in certain conditions.

Applying the operation can produce non-simply connected spaces.

The propositions are proven within the paper.

Abstract

We consider the operation to crush a subset of a manifold to one-point when the result of the crushing also be a manifold. Then the Poincare conjecture is split to two problems; for any closed orientable 3-manifold which is not homeomorphic to the sphere, one is that this operation preserve simply-connectedness, and another one is that we can get a non-simply connected space by applying the operation. We show these propositions in this paper.