Abstract: The structure of the first homology group of a cyclic covering of a knot is an important invariant well known in the knot theory. In the last century, H. Seifert developed a general approach to compute the homology group of the covering. Based on his ideas R. Fox found explicit form for H_1(M_n, Z), where Mn is an n-fold cyclic covering over a knot K admitting genus one Seifert surface. Present report shows the way to find the structure of H_1(M_n, Z) for 2-bridge knots admitting genus two Seifert surface. The result is given explicitly in terms of Alexander polynomial of the knot.

Cite: Медных И.А.
Теоремы Планса для групп гомологий двухмостовых узлов
"Дни геометрии в Новосибирске" 28 авг. - 1 сент. 2023