On volumes of arithmetic quotients of PO(n,1), n odd

TL;DR

This paper determines the minimal volume of arithmetic hyperbolic orientable orbifolds in all odd dimensions greater than three, completing the minimal volume classification for these geometric objects.

Contribution

It provides a complete solution to the minimal volume problem for arithmetic hyperbolic n-orbifolds in all odd dimensions n>3.

Findings

Minimal volumes of arithmetic hyperbolic orientable orbifolds are explicitly determined for all odd n>3.

The results unify and extend previous partial classifications.

The minimal volume orbifolds are characterized in each dimension.

Abstract

We determine the minimal volume of arithmetic hyperbolic orientable n-dimensional orbifolds (compact and non-compact) for every odd dimension n>3. Combined with the previously known results it solves the minimal volume problem for arithmetic hyperbolic n-orbifolds in all dimensions.