On Pierce-like idempotents and Hopf invariants
Given a set K with cardinality ‖K‖ =n, a wedge decomposition of a space Y indexed by K, and a cogroup A, the homotopy group G=[A,Y] is shown, by using Pierce-like idempotents, to have a direct sum decomposition indexed by P(K)−{ϕ} which is strictly functorial if G is abelian. Given a class ρ:X→Y, th...
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| Format: | Article |
| Language: | English |
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Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S016117120330331X |
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| _version_ | 1832556600358862848 |
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| author | Giora Dula Peter Hilton |
| author_facet | Giora Dula Peter Hilton |
| author_sort | Giora Dula |
| collection | DOAJ |
| description | Given a set K with cardinality ‖K‖ =n, a wedge
decomposition of a space Y indexed by K, and a cogroup A,
the homotopy group G=[A,Y] is shown, by using Pierce-like
idempotents, to have a direct sum decomposition indexed by
P(K)−{ϕ} which is strictly functorial if G is abelian.
Given a class ρ:X→Y, there is a Hopf invariant
HIρ on [A,Y] which extends Hopf's definition when ρ is a comultiplication. Then HI=HIρ is a functorial sum of HIL over L⊂K, ‖L‖ ≥2. Each HIL is a
functorial composition of four functors, the first depending only
on An+1, the second only on d, the third only on ρ,
and the fourth only on Yn. There is a connection here with
Selick and Walker's work, and with the Hilton matrix calculus, as
described by Bokor (1991). |
| format | Article |
| id | doaj-art-2b3ed8e4873b456aa6fded66fe9a4e64 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-2b3ed8e4873b456aa6fded66fe9a4e642025-02-03T05:44:54ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-012003623903392010.1155/S016117120330331XOn Pierce-like idempotents and Hopf invariantsGiora Dula0Peter Hilton1Netanya College, P.O. Box 120, Neot Ganim, Netanya 42365, IsraelDepartment of mathematical Sciences, State University of New York at Binghamton, 13902-6000, NY, USAGiven a set K with cardinality ‖K‖ =n, a wedge decomposition of a space Y indexed by K, and a cogroup A, the homotopy group G=[A,Y] is shown, by using Pierce-like idempotents, to have a direct sum decomposition indexed by P(K)−{ϕ} which is strictly functorial if G is abelian. Given a class ρ:X→Y, there is a Hopf invariant HIρ on [A,Y] which extends Hopf's definition when ρ is a comultiplication. Then HI=HIρ is a functorial sum of HIL over L⊂K, ‖L‖ ≥2. Each HIL is a functorial composition of four functors, the first depending only on An+1, the second only on d, the third only on ρ, and the fourth only on Yn. There is a connection here with Selick and Walker's work, and with the Hilton matrix calculus, as described by Bokor (1991).http://dx.doi.org/10.1155/S016117120330331X |
| spellingShingle | Giora Dula Peter Hilton On Pierce-like idempotents and Hopf invariants International Journal of Mathematics and Mathematical Sciences |
| title | On Pierce-like idempotents and Hopf invariants |
| title_full | On Pierce-like idempotents and Hopf invariants |
| title_fullStr | On Pierce-like idempotents and Hopf invariants |
| title_full_unstemmed | On Pierce-like idempotents and Hopf invariants |
| title_short | On Pierce-like idempotents and Hopf invariants |
| title_sort | on pierce like idempotents and hopf invariants |
| url | http://dx.doi.org/10.1155/S016117120330331X |
| work_keys_str_mv | AT gioradula onpiercelikeidempotentsandhopfinvariants AT peterhilton onpiercelikeidempotentsandhopfinvariants |