B Is the 10 Dimensional Poincaré Group a Coincidence?

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The Poincaré group and M-theory both have 10 dimensions
Is this a coincidence?
 
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Paige_Turner said:
Summary:: The Poincaré group and M-theory both have 10 dimensions

Is this a coincidence?
Yes. And there isn't even a defined single dimension for an M-theory, since there are several different concepts unified in M-theory. In any case, M-theory generalizes string theories, which involve super Lie algebras. The Poincaré group has a classical Lie algebra and moreover isn't semisimple.
 


Well, it depends on what you're referring to as a coincidence. Can you provide more context or information? Without more details, it's difficult to say whether or not something is a coincidence.
 

Thread '2-sphere intrinsic definition by gluing disks' boundaries'

A sphere as topological manifold can be defined by gluing together the boundary of two disk. Basically one starts assigning each disk the subspace topology from ##\mathbb R^2## and then taking the quotient topology obtained by gluing their boundaries. Starting from the above definition of 2-sphere as topological manifold, shows that it is homeomorphic to the "embedded" sphere understood as subset of ##\mathbb R^3## in the subspace topology.
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