On Pierce-like idempotents and Hopf invariants
2003 ◽
Vol 2003
(62)
◽
pp. 3903-3920
Keyword(s):
Given a setKwith cardinality‖K‖ =n, a wedge decomposition of a spaceYindexed byK, and a cogroupA, the homotopy groupG=[A,Y]is shown, by using Pierce-like idempotents, to have a direct sum decomposition indexed byP(K)−{ϕ}which is strictly functorial ifGis abelian. Given a classρ:X→Y, there is a Hopf invariantHIρon[A,Y]which extends Hopf's definition whenρis a comultiplication. ThenHI=HIρis a functorial sum ofHILoverL⊂K,‖L‖ ≥2. EachHILis a functorial composition of four functors, the first depending only onAn+1, the second only ond, the third only onρ, and the fourth only onYn. There is a connection here with Selick and Walker's work, and with the Hilton matrix calculus, as described by Bokor (1991).
Keyword(s):
1998 ◽
Vol 21
(2)
◽
pp. 433-440
◽
1995 ◽
Vol 138
◽
pp. 113-140
◽
2009 ◽
Vol 21
(1)
◽
pp. 1-19
◽
1998 ◽
Vol 50
(3)
◽
pp. 525-537
◽