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Harmonic Representatives in Homology over Arbitrary Fields by Catanzaro, Michael J.; Vose, Brantley is a scholarly article available to read on EtoBox.

What is Harmonic Representatives in Homology over Arbitrary Fields about?

We introduce a notion of harmonic chain for chain complexes over fields of positive characteristic. A list of conditions for when a Hodge decomposition theorem holds in this setting is given and we apply this theory to finite CW complexes. An explicit construction of the harmonic chain within a homology class is described when applicable. We show how the coefficients of usual discrete harmonic chains due to Eckmann can be reduced to localizations of the integers, allowing us to compare classical harmonicity with the notion introduced here. We focus on applications throughout, including CW decompositions of orientable surfaces and examples of spaces arising from sampled data sets.

Author

Catanzaro, Michael J.; Vose, Brantley

Published

2021

Language

EN