Abstract
Consider two cubical sets X and Y. In Chapter 2 we have studied the associated homology groups H*(X) and H*(Y). Now assume that we are given a continuous map f: X → Y. It is natural to ask if f induces a group homomorphism f*: H*(X) → H*(Y). If so, do we get useful information out of it? The answer is yes and we will spend the next three chapters explaining how to define and compute f*. It is worth noting, even at this very preliminary stage, that since H*(X) and H*(Y) are abelian groups, f* is essentially a linear map and therefore, from the algebraic point of view, easy to use.
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© 2004 Springer-Verlag New York, Inc.
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Kaczynski, T., Mischaikow, K., Mrozek, M. (2004). Preview of Maps. In: Computational Homology. Applied Mathematical Sciences, vol 157. Springer, New York, NY. https://doi.org/10.1007/0-387-21597-2_5
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DOI: https://doi.org/10.1007/0-387-21597-2_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2354-7
Online ISBN: 978-0-387-21597-6
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