Timeline for answer to Conceptual reason why the sign of a permutation is well-defined? by manzana
Current License: CC BY-SA 4.0
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| when toggle format | what | by | license | comment | |
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| Mar 13, 2022 at 16:04 | comment | added | Vitali Kapovitch | It seems to me that it's easier to do induction on the bundle $O(n-1)\to O(n)\to S^{n-1}$. From the long exact homotopy sequence it follows that the inclusion $O(n-1)\to O(n)$ gives a bijection on $\pi_0$ if $n\ge 3$. This reduces everything to $O(2)$ which is easy to deal with by hand. | |
| Mar 11, 2022 at 3:28 | history | edited | manzana | CC BY-SA 4.0 |
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| Mar 10, 2022 at 22:57 | comment | added | manzana | Edited, hopefully I've clarified things. | |
| Mar 10, 2022 at 22:56 | history | edited | manzana | CC BY-SA 4.0 |
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| Mar 10, 2022 at 21:51 | comment | added | wlad | "In this way it is straightforward to see that the set of sets of n−1 orthogonal vectors is connected" - I don't see how | |
| Mar 10, 2022 at 3:22 | history | answered | manzana | CC BY-SA 4.0 |