1993 | OriginalPaper | Buchkapitel
Locally effective objects and algebraic topology
verfasst von : Julio Rubio, Francis Sergeraert
Erschienen in: Computational Algebraic Geometry
Verlag: Birkhäuser Boston
Enthalten in: Professional Book Archive
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Algebraic topology consists of associating invariants are of an algebraic nature, describing certain topological properties. For example, since Poincaré, it is known how to associate the group π1(X,x0 to a topological space X and to one of its points x0; this group is called the Poincaré group or the first homotopy group of the space X based on x0. This group is null if and only if the space X is simply connected at x0; in another case, the group measures the lack of simple connectivity. Many other groups can be associated to a topological space, evaluating certain properties of this space: homology groups,K-theory groups,etc.