Geometry & Topology
- Geom. Topol.
- Volume 9, Number 2 (2005), 971-990.
End reductions, fundamental groups, and covering spaces of irreducible open 3–manifolds
Suppose is a connected, open, orientable, irreducible 3–manifold which is not homeomorphic to . Given a compact 3–manifold in which satisfies certain conditions, Brin and Thickstun have associated to it an open neighborhood called an end reduction of at . It has some useful properties which allow one to extend to various results known to hold for the more restrictive class of eventually end irreducible open 3–manifolds.
In this paper we explore the relationship of and with regard to their fundamental groups and their covering spaces. In particular we give conditions under which the inclusion induced homomorphism on fundamental groups is an isomorphism. We also show that if has universal covering space homeomorphic to , then so does .
This work was motivated by a conjecture of Freedman (later disproved by Freedman and Gabai) on knots in which are covered by a standard set of lines in .
Geom. Topol., Volume 9, Number 2 (2005), 971-990.
Received: 14 July 2004
Revised: 18 May 2005
Accepted: 18 May 2005
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57M10: Covering spaces
Secondary: 57N10: Topology of general 3-manifolds [See also 57Mxx] 57M27: Invariants of knots and 3-manifolds
Myers, Robert. End reductions, fundamental groups, and covering spaces of irreducible open 3–manifolds. Geom. Topol. 9 (2005), no. 2, 971--990. doi:10.2140/gt.2005.9.971. https://projecteuclid.org/euclid.gt/1513799609