Poincaré’s conjecture (proved by G. Perelman) interpreted by the isomorphism of Minkowski space and the separable complex Hilbert space

The Poincaré conjecture proved by G. Perelman is one of the seven problems declared by Clay Mathematics Institute as “Millennium Problems”. It is a topological statement, unproved about a century, which links an object in 4-dimensional Euclidean space such as the unit 3-sphere to the 3-dimensional Euclidean space itself. An interpretation of the Poincaré statement is intended by two basic mathematical structure furthermore underlying two of the most fundamental physical theories such as special relativity and quantum mechanics. Thus, a pathway to the physical meaning is traced. That interpretative reformulation suggest an idea for another proof grounded on physical intuition.

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