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Affine Flows on 3-Manifolds
Shigenori Matsumoto, Nihon University, Tokyo, Japan

Memoirs of the American Mathematical Society
2003; 94 pp; softcover
Volume: 162
ISBN-10: 0-8218-3257-3
ISBN-13: 978-0-8218-3257-8
List Price: US$60
Individual Members: US$36
Institutional Members: US$48
Order Code: MEMO/162/771
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In this paper, we consider nonsingular flows on closed 3-manifolds which are transversely modeled on the real affine geometry of the plane. We obtain classification results for the following three types of flows. (1) Flows whose developing maps are \(\mathbb{R}\)-bundle maps over \(\mathbb{R}^2\). (2) Flows whose holonomy groups are contained in \(SL(2,\mathbb{R})\). (3) Flows with homotopy lifting property whose holonomy groups are contained in \(SL(2,\mathbb{R})\ltimes \mathbb{R}\).


Graduate students and research mathematicians interested in geometry and topology.

Table of Contents

  • Introduction
  • Complete affine flows
  • Luxuriant foliations
  • SL-flows
  • SA-flows
  • Bibliography
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