Abstract
We have presented in this book a theory of cubical homology. Our justification for this approach lies in the applications described in Chapters 1, 8, and 10, where we are required to work with large sets of data and for which we need a computationally effective means of computing homology. In all these examples the data itself naturally generates cubical sets. However, this cubical homology theory is unconventional, and furthermore, there is a wide variety of other homology theories available.KeywordsSimplicial ComplexChain ComplexSimplicial TheoryCategory TheoryAlgebraic TopologyThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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