LINKING OF RANDOM p-SPHERES IN Zd

Author:

SOTEROS C. E.1,SUMNERS D. W.2,WHITTINGTON S. G.3

Affiliation:

1. Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, Sask., Canada S7N 0W0, Canada

2. Department of Mathematics, Florida State University, Tallahassee, Florida 32306-3027, U.S.A.

3. Department of Chemistry, University of Toronto, Toronto, Ontario, Canada M5S 1A1, Canada

Abstract

We consider the number of embeddings of k p-spheres in Zd, with p+2≤d≤2p+1, stratified by the p-dimensional volumes of the spheres. We show for p+2<d that the number of embeddings of a fixed link type of k equivolume p-spheres grows with increasing p-dimensional volume at an exponential rate which is independent of the link type. For d=p+2 we derive similar results both for links of unknotted p-spheres and for "augmented" links where each component p-sphere can have any knot type, and similar but weaker results when the spheres are of specified knot type.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Reference13 articles.

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