You can use the exact sequence of homotopy groups you mention (without knowing the maps) to get the result once you know $\pi_1(SO(3))$.

2015年11月18日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

2017年10月3日 · I have known the data of $\pi_m(SO(N))$ from this Table: I wonder whether there are some useful information that I can relate $\pi_m(SO(N))$ and $\pi_m(O(N))$?

2017年4月24日 · $\begingroup$ Well, to answer your question, you should show that $\mathfrak{so}(n)$ consists of skew-symmetric matrices (I am sweeping something under the rug here, because you need to lower one index of an element of $\mathfrak{so}(n)$ in order to get a skew-symmetric matrix with two indices down).

2024年12月16日 · So I take your questions to be the following, rephrased from the end of your post: You want to know why $\ker N:\Gamma(\Phi)\to\mathbb{R}^\times$ defines a Lie group

2016年5月27日 · For example, suppose there is a social science study on 2 child families with at least 1 daughter-- in this situation, about 1/3 of the families will be daughter-daughter, 1/3 will be daughter-son, and 1/3 will be son-daughter. You have to consider the full probability space of two trials (d-d,d-s,s-d,s-s) and eliminate the s-s possibility.

The standard circle is drawn with the 0 degree starting point at the intersection of the circle and the x-axis with a positive angle going in the counter-clockwise direction.

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2021年2月6日 · $\begingroup$ They are actually different concepts. "Faithful" means that there is no kernel (i.e, no element different from the identity fixes all elements of your set), whereas "free" means that the action of any element different from the identity is fixed-point free. $\endgroup$

2017年8月26日 · It seems to me that perpendicular, orthogonal and normal are all equivalent in two and three dimensions. I'm curious as to which situations you would want to use one term over the other in two and...