Lie Groups and Lie Algebras: Lesson 37 - The Fundamental Groups of SU(2) and SO(3)

Lie Groups and Lie Algebras: Lesson 37 - Homotopy Groups of SU(2) and SO(3)

In this lesson we discover the Fundamental Group of SU(2) and S0(3) and learn the critical fact that they are not the same. That is, the Fundamental Group associated with the topological space SU(2) is simply connected and the Fundamental Group associated with the topological space SO(3) is doubly connected. This is a critical fact and has a deep relationship to the fact that SU(2) and SO(3) were generated by the same Lie Algrebras. Our next lessons will begin to explore that connection.

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Lie Algebra,Lie Groups,Homotopy,