3 Manifolds Which Are End 1 Movable
3 Manifolds Which Are End 1 Movable by Matthew G. Brin
English | 30 Dec. 1989 | ISBN: 0821824740 | 73 Pages | PDF | 10 MB
English | 30 Dec. 1989 | ISBN: 0821824740 | 73 Pages | PDF | 10 MB
This paper continues a series by the authors on non-compact 3-manifolds. We describe the structure, up to end homeomorphism, of those orientable, noncompact 3-manifolds in which all loops near oo homotop to oo while staying near oo (the proper homotopy condition "end 1-movability" of the title). This extends previous work by others and by the authors because end 1-movability is weaker than properties studied before (such as 7Ti -stability, the main characterizing property of interiors of compact 3-manifolds), and also because our result is the first to analyse a class of non-compact 3-manifolds whose defining properties include neither irreducibility nor compact boundary. A corollary gives a new characterization of orientable, missing boundary 3-manifolds as those that are end 1-movable, and have finitely many summands and finitely generated first homology, and we relate this to J. Simon's problem of finding 3-manifold compactifications of 3-manifold covers.