Isometries of Orbifolds Double-Covered by Lens Spaces

Abstract

Let K be a two-bridge knot in S3. Then K is also denoted as the four-plat, b(p,q) to indicate its association with some rational number p/q. The lens space L = L(p,q) admits an isometry, τ, of order 2, such that the quotient space L modulo the involution τ is an orbifold whose exceptional set is K. In this paper, the isometries of these orbifolds are classified; this is equivalent to computing the isometries of (S3,K).