Bi-twist manifolds and two-bridge knots

TL;DR

This paper provides explicit face-pairing descriptions of all branched cyclic covers of the 3-sphere over two-bridge knots, demonstrating the efficiency of bi-twisted face-pairing constructions and applying them to fundamental group and homology computations.

Contribution

It introduces a uniform, explicit method using bi-twisted face-pairings for describing branched cyclic covers over two-bridge knots, enhancing computational approaches.

Findings

Explicit face-pairing descriptions for all such covers

Bi-twisted constructions are efficient and natural

Applications to fundamental group and homology calculations

Abstract

We give uniform, explicit, and simple face-pairing descriptions of all the branched cyclic covers of the 3-sphere, branched over two-bridge knots. Our method is to use the bi-twisted face-pairing constructions of Cannon, Floyd, and Parry; these examples show that the bi-twist construction is often efficient and natural. Finally, we give applications to computations of fundamental groups and homology of these branched cyclic covers.