Pontryagin cohomology operation
In mathematics, a Pontryagin cohomology operation is a cohomology operation taking cohomology classes in H2n(X,Z/prZ) to H2pn(X,Z/pr+1Z) for some prime p. When p=2 these operations were introduced by Pontryagin (1942) and were named Pontryagin squares by Whitehead (1949). They were generalized to arbitrary primes by Thomas (1956).
See also
References
- Browder, William; Thomas, E. (1962), "Axioms for the generalized Pontryagin cohomology operations", The Quarterly Journal of Mathematics. Oxford. Second Series 13 (1): 55–60, doi:10.1093/qmath/13.1.55, ISSN 0033-5606, MR0140103
- Malygin, S.N.; Postnikov, M.M. (2001), "Pontryagin square", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1556080104, http://www.encyclopediaofmath.org/index.php?title=p/p073810
- Pontryagin, L. (1942), "Mappings of the three-dimensional sphere into an n-dimensional complex", C. R. (Doklady) Acad. Sci. URSS (N. S.) 34: 35–37, MR0008135
- Thomas, Emery (1956), "A generalization of the Pontrjagin square cohomology operation", Proceedings of the National Academy of Sciences of the United States of America 42: 266–269, ISSN 0027-8424, JSTOR 89856, MR0079254
- Whitehead, J. H. C. (1949), "On simply connected, 4-dimensional polyhedra", Commentarii Mathematici Helvetici 22: 48–92, doi:10.5169/seals-19190, ISSN 0010-2571, MR0029171