A simplification problem in manifold theory
Geometric Topology
2018-09-03 v3
Abstract
Two smooth manifolds M and N are called R-diffeomorphic if their product with the real line are diffeomorphic. We consider the following simplification problem: does R-diffeomorphism imply diffeomorphism or homeomorphism? For compact manifolds, analysis of this problem relies on some of the main achievements of the theory of manifolds, in particular the h- and s-cobordism theorems in high dimensions and the spectacular more recent classification results in dimensions 3 and 4. This paper presents what is currently known about the subject as well as some new results about classifications of R-diffeomorphisms.
Cite
@article{arxiv.1802.03186,
title = {A simplification problem in manifold theory},
author = {Jean-Claude Hausmann and Bjørn Jahren},
journal= {arXiv preprint arXiv:1802.03186},
year = {2018}
}
Comments
35 pages. Small corrections and improvements following referee's suggestions. To appear in "L'Enseignement Math\'ematique"