# Postnikov square

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In [algebraic topology](/source/algebraic_topology), a '''Postnikov square''' is a certain [cohomology operation](/source/cohomology_operation) from a first [cohomology](/source/cohomology) [group](/source/group_(mathematics)) ''H''<sup>1</sup> to a third cohomology group ''H''<sup>3</sup>, introduced by {{harvs|txt|last=Postnikov|year=1949|authorlink=Mikhail Postnikov}}. {{harvtxt|Eilenberg|1952}} described a generalization taking classes in ''H''<sup>''t''</sup> to&nbsp;''H''<sup>2''t''+1</sup>.

==References==

*{{Citation | last1=Eilenberg | first1=Samuel | author1-link=Samuel Eilenberg | title=Proceedings of the International Congress of Mathematicians, Cambridge, Massachusetts, 1950, vol. 2 | chapter-url=http://mathunion.org/ICM/ICM1950.2/ | publisher=Amer. Math. Soc. | location=Providence, R.I. | mr=0045388 | year=1952 | chapter=Homotopy groups and algebraic homology theories | pages=350–353 | access-date=2011-04-08 | archive-url=https://web.archive.org/web/20110820183116/http://mathunion.org/ICM/ICM1950.2/ | archive-date=2011-08-20 | url-status=dead }} [https://web.archive.org/web/20170830054528/http://www.mathunion.org/ICM/ICM1950.2/Main/icm1950.2.0350.0353.ocr.pdf PDF]
*{{eom|title=Postnikov square|first=A.F.|last= Kharshiladze}}
*{{Citation | last1=Postnikov | first1=M. M. | title=The classification of continuous mappings of a three-dimensional polyhedron into a simply connected polyhedron of arbitrary dimension | language=Russian | mr=0029173 | year=1949 | journal=Doklady Akademii Nauk SSSR |series=New Series | volume=64 | pages=461–462}}

Category:Algebraic topology

{{abstract-algebra-stub}}

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Adapted from the Wikipedia article [Postnikov square](https://en.wikipedia.org/wiki/Postnikov_square) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Postnikov_square?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.