We introduce the concept of regular genus for n-dimensional links and knots, and study the topological properties of it. Some characterization theorems of the trivial knot are given. In particular, the only genus zero n-dimensional knot is proved to be homeomorphic with the trivial knot. Then the regular genus of a knot is proved to be related to the one-dimensional homology of the universal abelian covering of its complement. Some applications to low-dimensional links and a final section about connected sums of links complete the paper.

A genus for n-dimensional knots and links / Cavicchioli, Alberto. - In: COLLECTANEA MATHEMATICA. - ISSN 0010-0757. - STAMPA. - 36 (3):(1985), pp. 229-242.

A genus for n-dimensional knots and links

CAVICCHIOLI, Alberto
1985

Abstract

We introduce the concept of regular genus for n-dimensional links and knots, and study the topological properties of it. Some characterization theorems of the trivial knot are given. In particular, the only genus zero n-dimensional knot is proved to be homeomorphic with the trivial knot. Then the regular genus of a knot is proved to be related to the one-dimensional homology of the universal abelian covering of its complement. Some applications to low-dimensional links and a final section about connected sums of links complete the paper.
36 (3)
229
242
A genus for n-dimensional knots and links / Cavicchioli, Alberto. - In: COLLECTANEA MATHEMATICA. - ISSN 0010-0757. - STAMPA. - 36 (3):(1985), pp. 229-242.
Cavicchioli, Alberto
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/451022
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