Timeline for On the nilpotence of the attaching maps for $\mathbb C \mathbb P^\infty$
Current License: CC BY-SA 4.0
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| May 23 at 12:31 | comment | added | Tyler Lawson | (In fact you can always take $f^{\wedge (m+3)}$, and if $X$ is connected you can take $f^{\wedge (m+1)}$.) | |
| May 23 at 12:21 | comment | added | Tyler Lawson | Suppose $f: S^k \to X$ is a map, and factor $f^{\wedge(n+m)} = (f^{\wedge n} \wedge id^{\wedge m}) \circ (\Sigma^{nk} f^{\wedge m})$. If $f$ is stably smash-nilpotent, then you can pick $m$ sufficiently large so that $f^{\wedge m}$ is stably trivial, and then if $k > 0$ you can find $n$ sufficiently large so that $\Sigma^{nk} f^{\wedge m}$ is in the stable range. So stably smash-nilpotent does imply unstably smash-nilpotent, but possibly with a different exponent. | |
| May 22 at 20:25 | history | edited | Tim Campion | CC BY-SA 4.0 |
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| May 22 at 20:19 | history | edited | Tim Campion | CC BY-SA 4.0 |
added 259 characters in body
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| May 22 at 20:12 | history | asked | Tim Campion | CC BY-SA 4.0 |