Abstract
Continuous maps are used to compare topological spaces, linear maps play the same role for vector spaces, and homomorphisms are the tool for comparing abelian groups. It is, therefore, natural to introduce chain maps, which are maps between chain complexes. This notion permits us to compare different chain complexes in the same fashion that homomorphisms allow us to compare abelian groups. A homomorphism of abelian groups is required to preserve group addition. In a chain complex we have an additional operation: taking the boundary of a chain. Therefore, the definition of a chain map will also require that it preserves boundaries.
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© 2004 Springer-Verlag New York, Inc.
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Kaczynski, T., Mischaikow, K., Mrozek, M. (2004). Chain Maps and Reduction Algorithms. In: Computational Homology. Applied Mathematical Sciences, vol 157. Springer, New York, NY. https://doi.org/10.1007/0-387-21597-2_4
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DOI: https://doi.org/10.1007/0-387-21597-2_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2354-7
Online ISBN: 978-0-387-21597-6
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