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On the homology of the Harmonic Archipelago

Umed Karimov, Dušan Repovš (2012)

Open Mathematics

We calculate the singular homology and Čech cohomology groups of the Harmonic Archipelago. As a corollary, we prove that this space is not homotopy equivalent to the Griffiths space. This is interesting in view of Eda’s proof that the first singular homology groups of these spaces are isomorphic.

On the Kauffman-Harary conjecture for Alexander quandle colorings.

Soichiro Asami (2006)

Revista Matemática Complutense

The Kauffman-Harary conjecture is a conjecture for Fox's colorings of alternating knots with prime determinants. We consider a conjecture for Alexander quandle colorings by referring to the Kauffman-Harary conjecture. We prove that this new conjecture is true for twist knots.

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