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METRICS ON HOMOTOPY TYPES
A Thesis
Submitted to the Faculty
in partial ful llment of the requirements for the
degree of
Doctor of Philosophy
in
Mathematics
by
Nicholas A. Scoville
DARTMOUTH COLLEGE
Hanover, New Hampshire
June 2010
Examining Committee:
Martin Arkowitz, Chair
Vladimir Chernov
Je rey Strom
Jody Trout
Brian W. Pogue, Ph.D.
Dean of Graduate Studies
Object Description
| Call No. | Ph.D. 2010 c.2 |
| Author | Scoville, Nicholas A. |
| Title | Metrics on homotopy types. |
| Date | 2010 |
| Abstract | A metric structure on a set gives a concept of distance between any two elements of that set, and it induces a topology. In this thesis, we provide several ways to put a metric structure on the collection of CW complexes. We accomplish this by using the numerical invariants of cone length and Lusternik-Schnirelmann category as a framework and considering other topological invariants to determine the complexity of spaces. This leads us to the definition of a weighted length between spaces. After looking at several examples of weighted lengths and studying their properties, we investigate the induced metric structure and close by posing some open questions. |
| Description | ix, 102 leaves : ill. ; 28 cm. |
| Format | application/pdf |
| Advisor | Arkowitz, Martin A., Chernov, Vladimir, Strom, Jeff, Trout, John |
| Subject | Homotopy theory. CW complexes. |
| College | Dartmouth College. Dept. of Mathematics. |
| Issuing Body | Dartmouth Dissertations are made available through the Dartmouth Digital Library. |
| Degree | Thesis (Ph.D.)--Dartmouth College. |
| Copyright | All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means without permission in writing from the author. |
| DOI | http://dx.doi.org/10.1349/ddlp.371 |
Description
| Title | Page 1 |
| Format | application/pdf |
| Issuing Body | Dartmouth Dissertations are made available through the Dartmouth Digital Library. |
| Degree | Thesis (Ph.D.)--Dartmouth College. |
| Full Text | METRICS ON HOMOTOPY TYPES A Thesis Submitted to the Faculty in partial ful llment of the requirements for the degree of Doctor of Philosophy in Mathematics by Nicholas A. Scoville DARTMOUTH COLLEGE Hanover, New Hampshire June 2010 Examining Committee: Martin Arkowitz, Chair Vladimir Chernov Je rey Strom Jody Trout Brian W. Pogue, Ph.D. Dean of Graduate Studies |
