Division-Alebra/Poncare-Conjecture correspondence

TL;DR

This paper explores the potential deep connections between division algebras and the Poincaré conjecture, suggesting their combined relevance in mathematics and physics, especially in relativity, cosmology, and quantum systems.

Contribution

It proposes a novel framework linking division algebras and the Poincaré conjecture through torsion, and discusses their implications in physical theories and quantum generalizations.

Findings

Division algebras and Poincaré conjecture can be combined using torsion concepts.

Potential applications in special relativity and cosmology are discussed.

The conjecture may enable generalizations of Hopf maps via n-qubit systems.

Abstract

We briefly describe the importance of division algebras and Poincar\'e conjecture in both mathematical and physical scenarios. Mathematically, we argue that using the torsion concept one can combine the formalisms of division algebras and Poincar\'e conjecture. Physically, we show that both formalisms may be the underlying mathematical tools in special relativity and cosmology. Moreover, we explore the possibility that by using the concept of n-qubit system, such conjecture may allow generalization the Hopf maps.