Loops, waves, and an "algebra" for Heegaard splittings.

Title: Loops, waves, and an "algebra" for Heegaard splittings.
Identifier: AAI9946235
identifier: 9946235
Creator: Zablow, Joel.
Contributor: Adviser: Martin Bendersky
Date: 1999
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: In this thesis, I consider an algebraic structure involving isotopy classes simple closed curves (circles) on a closed orientable surface F. We may consider F to be the boundary of a handlebody H of genus g. I relate this to Heegaard splittings, (H 1, H2, F), of closed orientable 3-manifolds, M. The operations of this structure are used in the proof of topological results. In particular, I prove results about reducibility of splittings, characterization of loops on F bounding disks in Hi (i = 1,2), and properties of iterated connected sums. I also give a presentation of a subgroup of MCG(F) which preserves the number of waves of a given splitting, and use this to reprove a result of Homma, Ochiai, and Takahashi. A number of algebraic relations in the structure are detailed and some questions are asked about further connections between the algebra and the topology.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.