A Natural Isomorphism from the Ordered Homology to the Oriented Homology of an Injective Set
Date of Award
2009
Document Type
Thesis
Degree Name
Bachelors
Department
Natural Sciences
First Advisor
McDonald, Patrick
Keywords
Algebraic Topology, Simplicial Homology, Homological Algebra
Area of Concentration
Mathematics
Abstract
In the basic combinatorial topology of simplicial complexes, it has been proven that the ordered homology functor is naturally isomorphic to the oriented homology functor. In this thesis we generalize this result substantially. We prove that there is a natural isomorphism from the ordered homology to the oriented homology of the singular set functor associated to a well-behaved simplicial-type object in a category subject to some mild restrictions. While the author's literature review did not turn up this result, he makes no claims to originality.
Recommended Citation
Chandler, Nathaniel, "A Natural Isomorphism from the Ordered Homology to the Oriented Homology of an Injective Set" (2009). Theses & ETDs. 4073.
https://digitalcommons.ncf.edu/theses_etds/4073
Rights
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