Vol. 59, No. 2, 1975

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Generators for two groups related to the braid group

Hugh M. Hilden

Vol. 59 (1975), No. 2, 475–486

Let D be the unit ball in 3-space and let Ak be a set of k proper disjoint arcs in D lying in the x z plane. The group, 2k, of orientation preserving homeomorphisms of boundary D leaving the set Akboundary D invariant, modulo those isotopic to the identity via an isotopy fixing the set Akboundary D, is a natural homomorphic image of the 2k string braid group of the sphere via a homomorphism with kernel Z2.

In this paper, finite sets of generators are explicitly determined for the subgroups of 2k generated by

(1) homeomorphisms of D leaving the set Ak invariant, and

(2) homeomorphisms of D leaving the set Ak fixed pointwise.

Mathematical Subject Classification
Primary: 55A25
Received: 26 August 1974
Published: 1 August 1975
Hugh M. Hilden