# Cusps in 3d gravity Cusps are conical defects where the conical angle is taken to be zero. In this limit, the distance between any point and the tip of the cone becomes infinite. Cusped manifolds are non-compact but have finite volumes. In mathematics, hyperbolic knot complements are manifolds obtained by removing hyperbolic knots from the embedding manifolds, where the geometry is such that the knots are at the tip of the cusps. ## Refs - reviews - see e.g. Thurston's book - holography - [[2024#Grabovsky]]: massless scalar on conical backgrounds, including a discussion on the cusp limit - [[2025#Stanford, Yan]]: including cusps in the path integral to cancel divergences (works as a counter term)