Abstract
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,x 0 to a topological space X and to one of its points x 0; this group is called the Poincaré group or the first homotopy group of the space X based on x 0. This group is null if and only if the space X is simply connected at x 0; 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.
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© 1993 Birkhäuser Boston
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Rubio, J., Sergeraert, F. (1993). Locally effective objects and algebraic topology. In: Eyssette, F., Galligo, A. (eds) Computational Algebraic Geometry. Progress in Mathematics, vol 109. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-2752-6_17
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DOI: https://doi.org/10.1007/978-1-4612-2752-6_17
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