Revistes Catalanes amb Accés Obert (RACO)

A genus for $n$-dimensional knots and links

Alberto Cavicchioli


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.

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