Talk:Postnikov system
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Characteristic classes
[edit]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
[edit]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
[edit]"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
[edit]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 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)