Pontryagin cohomology operation
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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 number p. When p=2 these operations were introduced by Pontryagin (1942) and were named Pontrjagin squares by (Whitehead 1949) (with the term "Pontryagin square" also being used). They were generalized to arbitrary primes by (Thomas 1956).
See also
- Steenrod operation
References
- Browder, William; Thomas, E. (1962), "Axioms for the generalized Pontryagin cohomology operations", The Quarterly Journal of Mathematics, Second Series 13 (1): 55–60, doi:10.1093/qmath/13.1.55, ISSN 0033-5606
- Hazewinkel, Michiel, ed. (2001), "Pontryagin square", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4, https://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, New Series 34: 35–37
- 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 (5): 266–269, doi:10.1073/pnas.42.5.266, ISSN 0027-8424, PMID 16589865, Bibcode: 1956PNAS...42..266T
- Whitehead, J. H. C. (1949), "On simply connected, 4-dimensional polyhedra", Commentarii Mathematici Helvetici 22: 48–92, doi:10.1007/bf02568048, ISSN 0010-2571
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