Séminaire Algèbre Géométrie Algébrique Topologie Algébrique :

Le 22 septembre 2005 à 11:00 - salle 431

Présentée par Morisugi Kaoru - Université de Wakayama

Hopf Invariants after T. Ganea

James-Hopf invariants and Hilton-Milnor-Hopf invariants are both useful and important in both computations and theories of homotopy groups. Those invariants are defined on the suspension spaces. Some people including H.Toda, T.Ganea and B.Gray, wanted to extend to more general spaces where Hopf invariants can be defined. On the other hand, Boardman-Steer unified these invariants after enough suspension by taking the axiomatic approach. I will talk about these invariants following T. Ganea's approach, and also some interesting duality in the sense of Eckman-Hilton.
References T. Ganea: Generalization of homology and homotopy suspension, Comment. Math. Helv. 39 (1965). T. Ganea: On the homotopy suspension, Comment. Math. Helv. 43 (1968). Boardman-Steer: On Hopf invariants, Comment. Math. Helv. 42 (1965). B. Gray: On the homotopy groups of mapping cones, Proc. London Math.Soc (1973). Cornea-Lupton-Oprea-Tanea, in "Lusternik-Schnirelmann category", Math Survey vol. 13 AMS (2003).