A genus for N-dimensional knots and links

Autores: Alberto Cavicchioli
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 36, Fasc. 3, 1985, págs. 229-242
Idioma: inglés
Títulos paralelos:
- Un género para nudos y enlaces N-dimensionales
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Resumen
- The concept or regular tenus for $n$-dimensional links is introduced. It extends the classical genus of one-dimensional llinks. 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. Partial extensions for links of these results are also obtained. Some applications to low-dimensional links and a final section about connected sums of links complete the paper.