On the volume and the Chern-Simons invariant for the hyperbolic alternating knot orbifolds

TL;DR

This paper extends existing methods to provide explicit formulas for calculating the volume and Chern-Simons invariant of hyperbolic alternating knot orbifolds, enhancing understanding of their geometric properties.

Contribution

It introduces explicit formulae for volume and Chern-Simons invariants of hyperbolic alternating knot orbifolds, building on Neumann's methods.

Findings

Derived explicit formulas for volume calculations.

Provided formulas for Chern-Simons invariants.

Enhanced computational tools for hyperbolic orbifolds.

Abstract

We extend the Neumann's methods and give the explicit formulae for the volume and the Chern-Simons invariant for hyperbolic alternating knot orbifolds.