Titlebook: An Introduction to Algebraic Topology; Joseph J. Rotman Textbook 1988 Springer-Verlag New York Inc. 1988 Algebraic topology.CW complex.Fun

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CW Complexes,We return to homology, seeking to compute homology groups more effectively. The spaces for which this search is successful, the so-called CW complexes introduced by J. H. C. Whitehead, generalize simplicial complexes; they have also proved to be of fundamental importance in homotopy theory.

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Covering Spaces,When first computing .(.), we looked to winding numbers for inspiration.

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Long Exact Sequences,lgebraic. Let us now acquaint ourselves with the algebraic half of the definition in order to establish the existence of certain long exact sequences; these are very useful for calculation because they display connections between the homology of a space and the homology of its subspaces.

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https://doi.org/10.1007/978-3-658-10138-1this is not so). Many interesting spaces, as the torus, can be “triangulated”, and we shall see that this (strong) condition greatly facilitates calculation of homology groups. Moreover, we shall also be able to give a presentation of the fundamental groups of such spaces.

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