Periodic Hamiltonian flows on four dimensional manifolds / Yael Karshon.

Format:

Book

Author/Creator:

Karshon, Yael, 1964- author.

Series:

Memoirs of the American Mathematical Society ; no. 672.

Memoirs of the American Mathematical Society, 0065-9266 ; number 672

Language:

English

Subjects (All):

Flows (Differentiable dynamical systems).

Hamiltonian systems.

Four-manifolds (Topology).

Physical Description:

1 online resource (87 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [1999]

Language Note:

English

Summary:

This book is intended for graduate students and research mathematicians interested in global analysis, analysis on manifolds, and symplectic geometry.

Contents:

Intro

Contents

1. Introduction

2. Graphs

2.1. The graph

2.2. Kähler toric varieties

2.3. Push-forward measures

3. Metrics

3.1. Gradient spheres

3.2. Dependence on the metric

4. Uniqueness: Graph determines space

4.1. Building an equivariant diffeomorphism that respects the moment maps

4.2. Building an isomorphism

5. Isolated fixed points implies toric variety

6. Blowing-up

6.1. Equivariant symplectic blow-ups and blow-downs

6.2. Blowing down to a minimal space

6.3. Minimal spaces

7. Completing the classification

our spaces are Kähler

7.1. Algorithm

Appendix A. Local normal forms

Appendix B. Diffeomorphisms of the two-sphere

Appendix C. Computing a Kähler cone

References.

Notes:

"September 1999, volume 141, number 672 (second of 4 numbers)."

Includes bibliographical references (pages 69-71).

Description based on print version record.

ISBN:

1-4704-0263-7