Milnor-Thurston homology groups of the Warsaw Circle

Janusz Przewocki

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arXiv · 1403.1478

Milnor-Thurston homology groups of the Warsaw Circle

Janusz Przewocki

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Abstract

Milnor-Thurston homology theory is a construction of homology theory that is based on measures. It is known that it is equivalent to singular homology theory in case of manifolds and complexes. Its behaviour for non-tame spaces is still unknown. This paper provides results in this direction. We prove that Milnor-Thurston homology groups for the Warsaw Circle are trivial except for the zeroth homology group which is uncountable dimensional. Additionally, we prove that the zeroth homology group is non-Hausdorff for this space with respect a natural topology that was proposed by Berlanga.

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BibTeX RIS

Janusz Przewocki. 2014-03-06. Milnor-Thurston homology groups of the Warsaw Circle. https://arxiv.org/abs/1403.1478

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