Systole length in hyperbolic n-Manifolds

Abstract We show that the length R of a systole closed hyperbolic n -manifold $$(n \ge 3)$$ ( n ? 3 ) admitting triangulation by t -simplices can be bounded below function and , namely $$\begin{aligned} \frac{1}{2^{(nt)^{O(n^4t)} }} . \end{aligned}$$ R 1 2 t O 4 . do this finding relation between number diameter manifold giving explicit bounds for well known core curve Margulis tube its radius. prove same result finite volume manifolds, with similar but slightly more involved proof.