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I've heard $E$ is for entire space, $B$ is for base space, so what is $M$ for?

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  • $\begingroup$ No clue, manifold? $\endgroup$
    – Fernando Muro
    Commented Apr 6, 2012 at 10:04
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    $\begingroup$ I reckon E is not for "entire space", but for "étalé space" (étalé means "spread out"). $\endgroup$
    – Malte
    Commented Apr 6, 2012 at 11:44
  • $\begingroup$ Thom uses notation such as $M(SO(n))$ for the Thom space in his original papers, e.g., Quelques propriétés globales des variétés différentiables. Comment. Math. Helv. 28, (1954). 17–86. So presumably he is responsible for that notation. $\endgroup$
    – Charles Rezk
    Commented Apr 6, 2012 at 12:36
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    $\begingroup$ $T$ was already taken for tangent bundle, so $M$ is a pretty good 2nd fiddle. $\endgroup$
    – Ryan Budney
    Commented Apr 6, 2012 at 19:38
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    $\begingroup$ It seems that the earliest use is in Thom's paper: archive.numdam.org/article/SB_1951-1954__2__271_0.pdf $\endgroup$
    – John Klein
    Commented Apr 6, 2012 at 21:48

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