Enumerating spherical $n$-links

Madeleine Burkhart; Joel Foisy

doi:10.2140/involve.2018.11.195

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Home > Journals > Involve > Volume 11 > Issue 2 > Article

2018 Enumerating spherical $n$-links

Madeleine Burkhart, Joel Foisy

Involve 11(2): 195-206 (2018). DOI: 10.2140/involve.2018.11.195

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Abstract

We investigate spherical links: that is, disjoint embeddings of 1-spheres and 0-spheres in the 2-sphere, where the notion of a split link is analogous to the usual concept. In the quest to enumerate distinct nonsplit $n$ -links for arbitrary $n$ , we must consider when it is possible for an embedding of circles and an even number of points to form a nonsplit link. The main result is a set of necessary and sufficient conditions for such an embedding. The final section includes tables of the distinct embeddings that yield nonsplit $n$ -links for $4 \leq n \leq 8$ .