Timeline for Algebraic topology and homotopy theory with simplicial sets instead of topological spaces
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Nov 24, 2021 at 15:08 | vote | accept | user469290 | ||
| Nov 24, 2021 at 9:51 | comment | added | D.-C. Cisinski | That is a very good answer, but I think we could add that all the basic knowledge we have of the homotopy groups of spheres (e.g. $\pi_n(S^n)=\mathbb Z$, $\pi_i(S^n)=0$ for $i<n$, Serre's finiteness theorem) can be formulated and proved with simplicial sets. This counts as Algebraic Topology made possibly without spaces, I think. | |
| Nov 23, 2021 at 21:11 | comment | added | Denis Nardin | @user469290 I don't think there's "someone" who proved them first. Most of the point is that one can translate the original proofs seamlessly with some practice. | |
| Nov 23, 2021 at 21:08 | comment | added | user469290 | Thanks! Who first proved the analogues of Freudenthal suspension, Whitehead, Brown, Blakers-Massey for Kan complexes? | |
| Nov 23, 2021 at 20:55 | history | edited | Denis Nardin | CC BY-SA 4.0 |
Blakers
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| Nov 23, 2021 at 20:43 | history | edited | Denis Nardin | CC BY-SA 4.0 |
added 112 characters in body
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| Nov 23, 2021 at 20:36 | history | answered | Denis Nardin | CC BY-SA 4.0 |