# Explicit formulae for Chern-Simons invariants of the hyperbolic $J(2n,-2m)$ knot orbifolds

## TL;DR

This paper derives explicit formulas for the Chern-Simons invariants of hyperbolic double twist knot orbifolds, enhancing understanding of their geometric and topological properties.

## Contribution

It provides explicit formulae for Chern-Simons invariants of hyperbolic double twist knot orbifolds using the Schl"afli formula, a novel computational approach.

## Key findings

- Explicit formulas for Chern-Simons invariants derived
- Application of Schl"afli formula to cone-manifold structures
- Enhanced understanding of hyperbolic knot orbifolds

## Abstract

We calculate the Chern-Simons invariants of the hyperbolic double twist knot orbifolds using the Schl\"{a}fli formula for the generalized Chern-Simons function on the family of cone-manifold structures of double twist knots.