https://math.stackexchange.com/questions/123650/fundamental-group-of-the-special-orthogonal-group-son
Also, if I'm not mistaken, Steenrod gives a more direct argument in "Topology of Fibre Bundles," but he might be using the long exact sequence of a fibration (which you mentioned).
https://math.stackexchange.com/questions/1535100/dimension-of-son-and-its-generators
Nov 18, 2015 · The generators of $SO(n)$ are pure imaginary antisymmetric $n \\times n$ matrices. How can this fact be used to show that the dimension of $SO(n)$ is $\\frac{n(n-1
https://math.stackexchange.com/questions/3834980/irreducible-representations-of-son
Sep 21, 2020 · I'm looking for a reference/proof where I can understand the irreps of $SO(N)$. I'm particularly interested in the case when $N=2M$ is even, and I'm really only ...
https://math.stackexchange.com/questions/711492/prove-that-the-manifold-son-is-connected
The question really is that simple: Prove that the manifold $SO (n) \subset GL (n, \mathbb {R})$ is connected. it is very easy to see that the elements of $SO (n ...
https://math.stackexchange.com/questions/2455331/homotopy-groups-on-and-son-pi-mon-v-s-pi-mson
Oct 3, 2017 · I have known the data of $\\pi_m(SO(N))$ from this Table: $$\\overset{\\displaystyle\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\quad\\textbf{Homotopy …
https://math.stackexchange.com/questions/20506/representation-theory-of-son
Regarding the downvote: I am really sorry if this answer sounds too harsh, but math.SE is not the correct place to ask this kind of questions which amounts to «please explain the
https://math.stackexchange.com/questions/2249829/lie-algebra-of-son
Apr 24, 2017 · Welcome to the language barrier between physicists and mathematicians. Physicists prefer to use hermitian operators, while mathematicians are not biased towards her
https://math.stackexchange.com/questions/1781273/homotopic-type-of-gln-sln-and-son
I don't believe that the tag homotopy-type-theory is warranted, unless you are looking for a solution in the new foundational framework of homotopy type theory. It sure would be an
https://math.stackexchange.com/questions/1796298/is-son-actuallly-the-same-as-on
May 23, 2016 · $SO(n)$ is defined to be a subgroup of $O(n)$ whose determinant is equal to 1. In fact, the orthogonality of the elements of $O(n)$ demands that all of its members
https://math.stackexchange.com/questions/4897623/q-18-from-a-first-course-in-probability-by-sheldon-ross
Apr 12, 2024 · Each of 20 families selected to take part in a treasure hunt consist of a mother, father, son, and daughter. Assuming that they look for the treasure in pairs that