International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2003 / Article

Open Access

Volume 2003 |Article ID 583146 |

Giora Dula, Peter Hilton, "On Pierce-like idempotents and Hopf invariants", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 583146, 18 pages, 2003.

On Pierce-like idempotents and Hopf invariants

Received03 Mar 2003


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:XY, 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 LK, L2. 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).

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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