Author: Matthew G. Brin

Publisher: American Mathematical Soc.

Published: 1989

Total Pages: 86

ISBN-13: 0821824740

This paper continues a series by the authors on non-compact 3-manifolds. We describe the structure, up to end homeomorphism, of those orientable, non-compact 3-manifolds in which all loops near infinity [symbol] homotop to infinity [symbol] while staying near infinity [symbol] (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, and also because our result is the first to analyse a class of non-compact 3-manifolds whose defining properties include neither irreducibilty nor compact boundary. Our main tool is the end reduction--introduced in our earlier papers, developed further. End reductions are "simple" approximations of a non-compact 3-manifold that capture many of the manifold's properties.