On Pierce-like idempotents and Hopf invariants

Giora Dula and Peter Hilton

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-18

Abstract:

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 HI ρ on [ A , Y ] which extends Hopf's definition when ρ is a comultiplication. Then HI = HI ρ is a functorial sum of HI L over L ⊂ K , ‖ L ‖ ≥ 2 . Each HI L is a functorial composition of four functors, the first depending only on A n + 1 , the second only on d , the third only on ρ , and the fourth only on Y n . There is a connection here with Selick and Walker's work, and with the Hilton matrix calculus, as described by Bokor (1991).

Date: 2003
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/2003/583146.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/2003/583146.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:583146

DOI: 10.1155/S016117120330331X

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().