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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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). |
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| ISSN: | 0161-1712 1687-0425 |