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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).
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 …
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 …
Apr 24, 2017 · Welcome to the language barrier between physicists and mathematicians. Physicists prefer to use hermitian operators, while mathematicians are not biased towards …
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 $\text {SO} (n-1)\subset\text {SO} (n)$, …
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 …