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
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, 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
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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
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, 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
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