S^2 × S^2...×S^2×S^2 is a Direct Product of S^2 - Hypertorus

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SUMMARY

The discussion centers on the mathematical concept of the direct product of spheres, specifically the notation S^2 × S^2...×S^2, which lacks a widely recognized name. Participants clarify that while S^1 × S^1...×S^1 is commonly referred to as a hypertorus, the same terminology does not apply to the product of S^2. It is noted that the notation T^n is typically used to denote the direct product of n copies of S^1, emphasizing the distinction between these two mathematical constructs.

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  • Knowledge of the notation for spheres, specifically S^n
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LagrangeEuler
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http://en.wikipedia.org/wiki/Torus

##S^1 \times S^1... \times S^1 \times S^1 ##
is hypertorus.
And what is
##S^2 \times S^2... \times S^2 \times S^2 ##?
 
Physics news on Phys.org
It doesn't have a name.

Also, nobody says "hypertorus". Typically one uses ##T^n## to mean the direct product of ##n## copies of ##S^1##.
 

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