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TABLE OF CONTENTS Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
 

Summary: TABLE OF CONTENTS
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
Abstract of the Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . ii
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Volume and topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 Volume decreases under Dehn filling . . . . . . . . . . . . . . . . . . 5
2.2 Normalization of the fundamental cycle . . . . . . . . . . . . . . . . 6
2.3 Non­Fibroid surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 Bounds on Dehn filling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1 Essential Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 Pleated Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3 Cusp area shrinks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.4 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
i

ABSTRACT OF THE DISSERTATION
Topology of Hyperbolic 3­Manifolds
by
Ian Agol

  

Source: Agol, Ian - Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago

 

Collections: Mathematics