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In mathematics, a **Pontryagin cohomology operation** is a cohomology operation taking cohomology classes in *H*^{2n}(*X*,**Z**/*p*^{r}**Z**) to *H*^{2pn}(*X*,**Z**/*p*^{r+1}**Z**) 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).

- 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, MR 0140103 - Malygin, S.N.; Postnikov, M.M. (2001) [1994], "Pontryagin square",
*Encyclopedia of Mathematics*, EMS Press - 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, MR 0008135 - 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, Bibcode:1956PNAS...42..266T, doi:10.1073/pnas.42.5.266, ISSN 0027-8424, JSTOR 89856, MR 0079254, PMC 528270, PMID 16589865 - Whitehead, J. H. C. (1949), "On simply connected, 4-dimensional polyhedra",
*Commentarii Mathematici Helvetici*,**22**: 48–92, doi:10.1007/bf02568048, ISSN 0010-2571, MR 0029171, S2CID 121723000