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I've found lots of different proofs that so(n) is path connected, but i'm trying to understand one i found on stillwell's book naive lie theory. It's fairly informal and talks about paths in a very To add some intuition to this, for vectors in rn r n, sl(n) s l (n) is the space of all the transformations with determinant 1 1, or in other words, all transformations that keep the volume constant.
What is the fundamental group of the special orthogonal group so(n) s o (n), n> 2 n> 2? The answer usually given is: But i would like to see a proof of that and an …
