Lecture Notes on Generalized Heegaard Splittings

Nonfiction, Science & Nature, Mathematics, Topology, Geometry
Cover of the book Lecture Notes on Generalized Heegaard Splittings by Martin Scharlemann, Jennifer Schultens, Toshio Saito, World Scientific Publishing Company
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Author: Martin Scharlemann, Jennifer Schultens, Toshio Saito ISBN: 9789813109131
Publisher: World Scientific Publishing Company Publication: April 25, 2016
Imprint: WSPC Language: English
Author: Martin Scharlemann, Jennifer Schultens, Toshio Saito
ISBN: 9789813109131
Publisher: World Scientific Publishing Company
Publication: April 25, 2016
Imprint: WSPC
Language: English

This book is part of the series of three books arise from lectures organized by Hitoshi Murakami at RIMS, Kyoto University in the summer of 2001. The lecture series was aimed at a broad audience that included many graduate students. Its purpose lay in familiarizing the audience with the basics of 3-manifold theory and introducing some topics of current research. The first portion of the lecture series was devoted to standard topics in the theory of 3-manifolds. The middle portion was devoted to a brief study of Heegaard splittings and generalized Heegaard splittings.

In the standard schematic diagram for generalized Heegaard splittings, Heegaard splittings are stacked on top of each other in a linear fashion. This can cause confusion in those cases in which generalized Heegaard splittings possess interesting connectivity properties. Fork complexes were invented in an effort to illuminate some of the more subtle issues arising in the study of generalized Heegaard splittings.

Contents:

  • Preliminaries
  • Definition and Examples of Heegaard Splittings
  • Properties of Heegaard Splittings
  • Two Theorems on Heegaard Splittings
  • Generalized Heegaard Splittings

Readership: Graduate students and researchers in topology.
Key Features:

  • This is the only book on the topic
  • It is more specialized than related books
  • It delves deeply into one subject
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This book is part of the series of three books arise from lectures organized by Hitoshi Murakami at RIMS, Kyoto University in the summer of 2001. The lecture series was aimed at a broad audience that included many graduate students. Its purpose lay in familiarizing the audience with the basics of 3-manifold theory and introducing some topics of current research. The first portion of the lecture series was devoted to standard topics in the theory of 3-manifolds. The middle portion was devoted to a brief study of Heegaard splittings and generalized Heegaard splittings.

In the standard schematic diagram for generalized Heegaard splittings, Heegaard splittings are stacked on top of each other in a linear fashion. This can cause confusion in those cases in which generalized Heegaard splittings possess interesting connectivity properties. Fork complexes were invented in an effort to illuminate some of the more subtle issues arising in the study of generalized Heegaard splittings.

Contents:

Readership: Graduate students and researchers in topology.
Key Features:

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