Higher-order polynomial invariants of 3-manifolds giving lower bounds for Thurston norm

We define a new infinite sequence of invariants, d&d1;n for n ≥ 0, of a group G that measure the size of the successive quotients of the derived series of G. In the case that G is the fundamental group of a 3-manifold, we obtain new 3-manifold invariants. These invariants are closely related to the topology of the 3-manifold. We show that they give lower bounds for the Thurston norm. Moreover, we show that they give better estimates for the Thurston norm than the previously known bounds given by the Alexander norm, d&d1;0 . To do this, we exhibit 3-manifolds whose Alexander norm is trivial but whose d&d1;n are strictly increasing and can be made arbitrarily large. Other applications are made to detecting 3-manifolds that fiber over S 1 and to detecting 4-manifolds that admit no symplectic structure.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Natural Sciences

Grantor

Rice University

Year dc:date.issued

2002

Author dc:creator

• Harvey, Shelly Lynn

Advisor dc:contributor.advisor

• Cochran, Tim D.

• Mathematics

Statement dc:rights

• Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1911/18088

OAI identifier oai:identifier

oai:repository.rice.edu:1911/18088