Talk:Postnikov system

Characteristic classes
Can you get all characteristic classes through the use of Postnikov systems? If so, do you know a reference for that? 13:00, 3 March 2008 (UTC)

False definition
The definition of postnikov tower is false: the correct definition can be found in hatcher and is the following: a postnikov tower for X is the given of 1) a sequence of spaces and maps p_n X_n \to X_n-1, such that \pi_k(X_n) = 0 for every k>n 2) n equivalences f_n : X \to X_n s.t. p_n \circ f_n = f_n-1

Moreover, there is no way to reconstruct a topological space by its homotopy groups: they are not sufficient (even up to weak homotopy equivalence) --93.66.195.134 (talk) 18:09, 18 September 2012 (UTC)

ambiguous sentence
"Every path-connected space has such a Postnikov system, and it is unique up to homotopy"

what does it mean "unique up to homotopy"? clarify please!--62.18.243.184 (talk) 14:05, 19 May 2014 (UTC)

References and construction
This page should go over the construction of Postnikov towers and give some examples of applications. Check out these notes for a decent overview of the construction: https://web.archive.org/web/20200213180540/https://www.math.purdue.edu/~zhang24/towers.pdf. It also gives a computation of $$\pi_4(S^3)$$ and also defines the whitehead tower. — Preceding unsigned comment added by Wundzer (talk • contribs) 20:40, 13 February 2020 (UTC)


 * Computations of higher homotopy groups from whitehead: https://web.archive.org/web/20170519125745/https://www.math.wisc.edu/~maxim/753f13w7.pdf
 * Another useful reference for computations http://www.people.fas.harvard.edu/~xiyin/Site/Notes_files/AT.pdf — Preceding unsigned comment added by Wundzer (talk • contribs) 01:57, 16 February 2020 (UTC)
 * Include construction for spectra — Preceding unsigned comment added by Wundzer (talk • contribs) 22:19, 13 February 2020 (UTC)

Other

 * https://mathoverflow.net/questions/275013/postnikov-type-tower-for-a-map-between-spaces
 * https://www.ams.org/journals/tran/1967-127-03/S0002-9947-1967-0210131-2/S0002-9947-1967-0210131-2.pdf

Higher groups

 * https://math.stackexchange.com/questions/1017142/is-there-an-interpretation-of-higher-cohomology-groups-in-terms-of-group-extensi
 * https://mathoverflow.net/questions/284041/why-is-the-definition-of-the-higher-homotopy-groups-the-right-one/284049#284049
 * https://ncatlab.org/nlab/show/Postnikov+system