Cobordism Theory and Poincare Conjecture

TL;DR

This paper presents a simplified proof of the Poincaré conjecture for 3-manifolds using cobordism and Morse theory techniques, confirming that every compact smooth simply connected 3-manifold is homeomorphic to the 3-sphere.

Contribution

It introduces a novel proof method combining cobordism and Morse theory to establish the Poincaré conjecture.

Findings

Proof confirms all compact smooth simply connected 3-manifolds are homeomorphic to 3-sphere

Simplifies previous complex proofs of the Poincaré conjecture

Demonstrates effectiveness of cobordism and Morse theory in topological problems

Abstract

In this paper, by use of techniques associated to cobordism theory and Morse theory,we give a simple proof of Poincare conjecture, i.e. Every compact smooth simply connected 3-manifold is homeomorphic to 3-sphere.