Postnikov square
From Encyclopedia of Mathematics
A cohomology operation of type 
, where 
and 
are Abelian groups with a fixed heteromorphism 
, i.e. a mapping such that the function
 |
is bilinear and 
. Let 
be an epimorphism and let 
be a free Abelian group. The Postnikov square for 
-cocycles is defined by the formula
 |
where 
is a cochain with coefficients in 
such that 
. A suspension of a Postnikov square is a Pontryagin square. For a simply-connected space 
, the Postnikov square for which 
, 
and 
is defined by composition with the Hopf mapping 
is used to classify the mappings of three-dimensional polyhedra into 
. Postnikov squares were introduced by M.M. Postnikov [1].
References
| [1] | M.M. Postnikov, "The classification of continuous mappings of a three-dimensional polyhedron into a simply connected polyhedron of arbitrary dimension" Dokl. Akad. Nauk SSSR , 64 : 4 (1949) pp. 461–462 (In Russian) |
How to Cite This Entry:
Postnikov square. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Postnikov_square&oldid=48261
Postnikov square. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Postnikov_square&oldid=48261
This article was adapted from an original article by A.F. Kharshiladze (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article