Pontryagin product: Difference between revisions
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In [[mathematics]], the '''Pontryagin product''', introduced by {{harvs|txt|last=Pontryagin|authorlink=Lev Pontryagin|year=1939}}, is a product on the homology of a [[topological space]] induced by a product on the topological space. Special cases include the Pontryagin product on the homology of an [[abelian group]], the Pontryagin product on an [[H-space]], and the Pontryagin product on a [[loop space]]. |
In [[mathematics]], the '''Pontryagin product''', introduced by {{harvs|txt|last=Pontryagin|first=Lev|authorlink=Lev Pontryagin|year=1939}}, is a product on the homology of a [[topological space]] induced by a product on the topological space. Special cases include the Pontryagin product on the homology of an [[abelian group]], the Pontryagin product on an [[H-space]], and the Pontryagin product on a [[loop space]]. |
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==References== |
==References== |
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*{{Citation | last1=Brown | first1=Kenneth S. | authorlink = Kenneth Brown (mathematician) | title=Cohomology of groups | url=https://books.google.com/books?id=PMqb2DppvCsC | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=[[Graduate Texts in Mathematics]] | isbn=978-0-387-90688-1 |mr=672956 | year=1982 | volume=87}} |
*{{Citation | last1=Brown | first1=Kenneth S. | authorlink = Kenneth Brown (mathematician) | title=Cohomology of groups | url=https://books.google.com/books?id=PMqb2DppvCsC | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=[[Graduate Texts in Mathematics]] | isbn=978-0-387-90688-1 |mr=672956 | year=1982 | volume=87}} |
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*{{Citation | last1=Pontrjagin | first1= |
*{{Citation | last1=Pontrjagin | first1=Lev | authorlink = Lev Pontryagin | title=Homologies in compact Lie groups |mr=0001563 | year=1939 | journal=Rec. Math. N. S. [Mat. Sbornik] | volume=6 | issue = 48 | pages=389–422}} |
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[[Category:Homology theory]] |
[[Category:Homology theory]] |
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[[Category:Group theory]] |
[[Category:Group theory]] |
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{{topology-stub}} |
{{topology-stub}} |
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Revision as of 02:45, 3 March 2018
In mathematics, the Pontryagin product, introduced by Lev Pontryagin (1939), is a product on the homology of a topological space induced by a product on the topological space. Special cases include the Pontryagin product on the homology of an abelian group, the Pontryagin product on an H-space, and the Pontryagin product on a loop space.
References
- Brown, Kenneth S. (1982), Cohomology of groups, Graduate Texts in Mathematics, vol. 87, Berlin, New York: Springer-Verlag, ISBN 978-0-387-90688-1, MR 0672956
- Pontrjagin, Lev (1939), "Homologies in compact Lie groups", Rec. Math. N. S. [Mat. Sbornik], 6 (48): 389–422, MR 0001563
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