Area-contracting maps between rectangles
Name
61207020-MIT.pdf
Description
Full printable version
Size
11.79 MB
Format
Adobe PDF
Checksum (MD5)
788e2113627e3040d3a5a1c3cd32936b
Author(s)
Guth, Lawrence
Advisor(s)
Tomasz S. Mrowka.
Date Issued
2005
Publisher
Massachusetts Institute of Technology
Abstract
In this thesis, I worked on estimating the smallest k-dilation of all diffeomorphisms between two n-dimensional rectangles R and S. I proved that for many rectangles there are highly non-linear diffeomorphisms with much smaller k-dilation than any linear diffeomorphism. When k is equal to n-l, I determined the smallest k-dilation up to a constant factor. For all values of k and n, I solved the following related problem up to a constant factor. Given n-dimensional rectangles R and S, decide if there is an embedding of S into R which maps each k-dimensional submanifold of S to an image with larger k-volume. I also applied the k-dilation techniques to two purely topological problems: estimating the Hopf invariant of a map from a 3-manifold to a high-genus surface, and determining whether there is a map of non-zero degree from a 3-manifold to a hyperbolic 3-manifold.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.
Includes bibliographical references (p. 207-208).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.
Persistent DSpace Link
