Abstract
We finished the previous chapter with the observation that given a space X and a subset A it would be useful to have a means of computing the number of components of X that are disjoint from A. Using this as motivation, in Section 9.1 we introduce the concept of relative homology. Though motivated by a simple problem, it turns out that relative homology is an extremely powerful tool, both as a means of extracting topology from the homological algebra and as an abstract computational technique. The language of these computational methods takes the form of exact sequences, which are discussed in Section 9.2.
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© 2004 Springer-Verlag New York, Inc.
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Kaczynski, T., Mischaikow, K., Mrozek, M. (2004). Homological Algebra. In: Computational Homology. Applied Mathematical Sciences, vol 157. Springer, New York, NY. https://doi.org/10.1007/0-387-21597-2_9
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DOI: https://doi.org/10.1007/0-387-21597-2_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2354-7
Online ISBN: 978-0-387-21597-6
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