A Simple Proof On Poincar\'e Conjecture

TL;DR

This paper presents a straightforward proof of the Poincaré Conjecture, establishing that any compact smooth 3-manifold homotopically equivalent to a 3-sphere is actually diffeomorphic to it.

Contribution

It offers a simplified proof of the Poincaré Conjecture, a fundamental problem in topology, providing new insights into 3-manifold classification.

Findings

Proof confirms the conjecture for all compact smooth 3-manifolds homotopically equivalent to S^3

Establishes diffeomorphism between such manifolds and S^3

Simplifies previous complex proofs of the conjecture

Abstract

We give a simple proof on the Poincar\'e's conjecture which states that every compact smooth $3-$manifold which is homotopically equivalent to $S^3$ is diffeomorphic to $S^3$.