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edit approved Jun 4, 2016 at 19:50
Sean Lawton
edit approved Jun 4, 2016 at 19:50
Sean Lawton
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Explicit diffeomorphism between an infinite dimensional sphere and theirits product with itself

letLet $S$ be an infinite dimensional sphere in a Hillbert space. 

As $S$ is homotopic to the product $S \times S$, then $S$ is diffeomorphic to $S \times S$  (For hillbertfor Hilbert manifolds, homotopica homotopy equivalence implies diffeomorphism). 

Is there an explicit diffeomorphism between $S$ and $S \times S$?

Explicit diffeomorphism between infinite dimensional sphere and their product

let $S$ be an infinite dimensional sphere in a Hillbert space. As $S$ is homotopic to the product $S \times S$, then $S$ is diffeomorphic to $S \times S$(For hillbert manifolds, homotopic equivalence implies diffeomorphism). Is there an explicit diffeomorphism between $S$ and $S \times S$?

Explicit diffeomorphism between an infinite dimensional sphere its product with itself

Let $S$ be an infinite dimensional sphere in a Hillbert space. 

As $S$ is homotopic to the product $S \times S$, then $S$ is diffeomorphic to $S \times S$  (for Hilbert manifolds, a homotopy equivalence implies diffeomorphism). 

Is there an explicit diffeomorphism between $S$ and $S \times S$?

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Xiaoyang Chen
Xiaoyang Chen
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Explicit diffeomorphism between infinite dimensional sphere and their product

let $S$ be an infinite dimensional sphere in a Hillbert space. As $S$ is homotopic to the product $S \times S$, then $S$ is diffeomorphic to $S \times S$(For hillbert manifolds, homotopic equivalence implies diffeomorphism). Is there an explicit diffeomorphism between $S$ and $S \times S$?