A simplification problem in manifold theory
Jean-Claude Hausmann
Université de Genève, SwitzerlandBjørn Jahren
University of Oslo, Norway
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Abstract
Two smooth manifolds and are called -diffeomorphic if is diffeomorphic to . We consider the following simplication problem: does -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 classication results in dimensions 3 and 4. This paper presents what is currently known about the subject as well as some new results about classications of -diffeomorphisms.
Cite this article
Jean-Claude Hausmann, Bjørn Jahren, A simplification problem in manifold theory. Enseign. Math. 64 (2018), no. 1/2, pp. 207–248
DOI 10.4171/LEM/64-1/2-8