Kissing number in spherical space

Abstract: This paper investigates the behaviour of the kissing number $\kappa(n, r)$ of congruent radius $r > 0$ spheres in $\mathbb{S}^n$, for $n\geq 2$. Such a quantity depends on the radius $r$, and we plot the approximate graph of $\kappa(n, r)$ with relatively high accuracy by using new upper and lower bounds that are produced via semidefinite programming and by using spherical codes, respectively.