Author : Detlef Hardorp
Publisher : American Mathematical Soc.
ISBN 13 : 0821822330
Total Pages : 84 pages
Book Rating : 4.33/5 ( download)
Book Synopsis All Compact Orientable Three Dimensional Manifolds Admit Total Foliations by : Detlef Hardorp
Download or read book All Compact Orientable Three Dimensional Manifolds Admit Total Foliations written by Detlef Hardorp and published by American Mathematical Soc.. This book was released on 1980 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: A total foliation is an example of a geometric structure on a manifold. A total foliation of an [script]n dimensional manifold consists of a [script]n codimension one foliations that are transverse at every point. If a manifold admits a total foliation where all [script]n foliations are transverse oriented, it is said to be totally parallelizable. A necessary condition for total parallelizability is that the manifold be parallelizable. Whether or not this is also a sufficient condition is not known. In this memoir, the author proves a theorem: All compact orientable three dimensional manifolds admit total foliations. This theorem is proven by explicitly constructing total foliations for all compact orientable three manifolds