Timeline for $(-n-1)$-connected spectra vs. reduced excisive functors from $n$-truncated pointed spaces
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Aug 23, 2021 at 3:08 | comment | added | Emily | @MarcHoyois Oh right, I completely misunderstood Dmitri's answer. Also, the statement you mentioned about homotopy dimension goes precisely in the direction I wanted. Thanks! | |
| Aug 21, 2021 at 9:25 | history | edited | Marc Hoyois | CC BY-SA 4.0 |
fixed inequality
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| Aug 21, 2021 at 7:58 | comment | added | Marc Hoyois | $n$ became $-n$ in the middle of my previous comment, but hopefully what I meant is clear. | |
| Aug 21, 2021 at 7:47 | comment | added | Marc Hoyois | $n$-connective spectra are reduced excisive functors $\mathcal S^\mathrm{fin}_*\to\mathcal S$ that increase connectivity by at least $n$. A statement which I think goes in the direction you want is that such functors are determined by their restriction to finite wedges of spheres $S^k$ with $k\leq n$. In particular they are determined by their restriction to finite pointed spaces of homotopy dimension $\leq n$, which is very different from $n$-truncated spaces. | |
| Aug 21, 2021 at 7:38 | comment | added | Marc Hoyois | The case $n=0$ is far from true: every 1-excisive functor $\mathrm{Fin}_*\to \mathcal S$ is constant... | |
| Aug 20, 2021 at 22:31 | history | asked | Emily | CC BY-SA 4.0 |