Timeline for Notation: Why Ω for the based loop functor?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 26, 2017 at 19:39 | comment | added | Mark Grant | Morse's book "The Calculus of Variations in the Large" from 1934 uses $\Omega$ for the based loops in a manifold. | |
| Apr 24, 2017 at 14:43 | comment | added | Charles Rezk | The way he talks about it in the first paragraph makes me suspect he took the notation from Morse and/or Hurewicz, but I can't follow those references. | |
| Apr 24, 2017 at 14:37 | comment | added | Charles Rezk | Of course, I should have checked Serre first: he uses $\Omega_x$ for "based loops of $X$ at $x$" in his 1951 Annals paper about the Serre spectral sequence, for instance. | |
| Apr 24, 2017 at 14:31 | comment | added | Charles Rezk | It would help if we knew who chose that notation, and when they did. I don't know the answer. After poking around on MathSciNet, the earliest use of $\Omega$ for a loop space I can come up with is (MR0055683) G. Whitehead, "On the Freudenthal theorems" (Annals, 1953). He actually uses "$\Omega^{n+1}$" for what we call $\Omega S^{n+1}$. | |
| Apr 24, 2017 at 10:52 | comment | added | Todd Trimble | Wouldn't surprise me. Note also that $\Delta$ is used to denote the simplex category and objects therein, and $\Lambda$ a horn of a simplex. | |
| Apr 24, 2017 at 10:45 | review | First posts | |||
| Apr 24, 2017 at 10:46 | |||||
| Apr 24, 2017 at 10:43 | history | asked | user316092 | CC BY-SA 3.0 |