Fundamental group of the special orthogonal group 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).
A game problem about turn order based on the game state
Dec 14, 2025 · About two years ago I came up with this problem and I still can't find the solution, so I need help with it. Dad and his son are ordering a pizza. The pizza arrives and son cuts it …
lie groups - Lie Algebra of SO (n) - Mathematics Stack Exchange
Apr 24, 2017 · Where a, b, c, d ∈ 1, …, n a, b, c, d ∈ 1,, n. And so(n) s o (n) is the Lie algebra of SO (n). I'm unsure if it suffices to show that the generators of the ...
Why $\\operatorname{Spin}(n)$ is the double cover of $SO(n)$?
Dec 16, 2024 · You can let $\text {Spin} (n)$ act on $\mathbb {S}^ {n-1}$ through $\text {SO} (n)$. Since $\text {Spin} (n-1)\subset\text {Spin} (n)$ maps to $\text {SO} (n-1)\subset\text {SO} (n)$, …
Dimension of SO (n) and its generators - Mathematics Stack …
Nov 18, 2015 · The generators of SO(n) S O (n) are pure imaginary antisymmetric n × n n × n matrices. How can this fact be used to show that the dimension of SO(n) S O (n) is n(n−1) 2 n …
Prove that the manifold $SO(n)$ is connected
The question really is that simple: Prove that the manifold SO(n) ⊂ GL(n,R) S O (n) ⊂ G L (n, R) is connected. it is very easy to see that the elements of SO(n) S O (n) are in one-to-one …
Homotopy groups O(N) and SO(N): $\\pi_m(O(N))$ v.s.
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 …
How to find the difference between the son's and mother's age if …
Oct 23, 2019 · A son had recently visited his mom and found out that the two digits that form his age (eg :24) when reversed form his mother's age (eg: 42). Later he goes back to his place …
What is the relationship between SL (n) and SO (n)?
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 …
How connectedness of $O(n)$ or $SO(n)$ implies the …
Dec 7, 2024 · So, the quotient map from one Lie group to another with a discrete kernel is a covering map hence $\operatorname {Pin}_n (\mathbb R)\rightarrow\operatorname {Pin}_n …