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A note on singular homology groups of infinite products of compacta

Kazuhiro Kawamura (2002)

Fundamenta Mathematicae

Let n be an integer with n ≥ 2 and X i be an infinite collection of (n-1)-connected continua. We compare the homotopy groups of Σ ( i X i ) with those of i Σ X i (Σ denotes the unreduced suspension) via the Freudenthal Suspension Theorem. An application to homology groups of the countable product of the n(≥ 2)-sphere is given.

Category with a natural cone

Francisco Díaz, Sergio Rodríguez-Machín (2006)

Open Mathematics

Generally, in homotopy theory a cylinder object (or, its dual, a path object) is used to define homotopy between morphisms, and a cone object is used to build exact sequences of homotopy groups. Here, an axiomatic theory based on a cone functor is given. Suspension objects are associated to based objects and cofibrations, obtaining homotopy groups referred to an object and relative to a cofibration, respectively. Exact sequences of these groups are built. Algebraic and particular examples are given....

On the suspension homomorphism

S. Dragotti, G. Magro, L. Parlato (2002)

Bollettino dell'Unione Matematica Italiana

In this paper we investigate the conditions for the suspension homomorphism s : Θ r - 1 F S n - 1 , x 0 Θ r F S n , x 0 is onto or an isomorphism.

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