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 …

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 ...

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 ...

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).

Aug 19, 2025 · Diophantus' childhood ended at $14$, he grew a beard at $21$, married at $33$, and had a son at $38$. Diophantus' son died at $42$, when Diophantus himself was $80$, and so …

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 ...

Jul 29, 2020 · So the Problem goes like this :- An old man had $17$ camels . He had $3$ sons and the man had decided to give each son a property with his camels. Unfortunately however, the man dies, …

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 to ...

May 24, 2017 · Suppose that I have a group $G$ that is either $SU(n)$ (special unitary group) or $SO(n)$ (special orthogonal group) for some $n$ that I don't know. Which "questions ...

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 represnetation …