TY - JOUR

T1 - On Pierce-like idempotents and Hopf invariants

AU - Dula, Giora

AU - Hilton, Peter

PY - 2003

Y1 - 2003

N2 - 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)-(□) which is strictly functorial if G is abelian. Given a class p:X→Y, there is a Hopf invariant HIp on [A, Y] which extends Hopf's definition when p is a comultiplication. Then HI=HIp 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 A n+1, the second only on d, the third only on p, 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).

AB - 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)-(□) which is strictly functorial if G is abelian. Given a class p:X→Y, there is a Hopf invariant HIp on [A, Y] which extends Hopf's definition when p is a comultiplication. Then HI=HIp 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 A n+1, the second only on d, the third only on p, 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).

UR - http://www.scopus.com/inward/record.url?scp=17844367092&partnerID=8YFLogxK

U2 - 10.1155/S016117120330331X

DO - 10.1155/S016117120330331X

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AN - SCOPUS:17844367092

SN - 0161-1712

VL - 2003

SP - 3903

EP - 3920

JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

IS - 62

ER -