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Affine Flows on 3-Manifolds

Shigenori Matsumoto Nihon University, Tokyo, Japan
Available Formats:
Electronic ISBN: 978-1-4704-0369-0
Product Code: MEMO/162/771.E
94 pp
List Price: $60.00 MAA Member Price:$54.00
AMS Member Price: $36.00 Click above image for expanded view Affine Flows on 3-Manifolds Shigenori Matsumoto Nihon University, Tokyo, Japan Available Formats:  Electronic ISBN: 978-1-4704-0369-0 Product Code: MEMO/162/771.E 94 pp  List Price:$60.00 MAA Member Price: $54.00 AMS Member Price:$36.00
• Book Details

Memoirs of the American Mathematical Society
Volume: 1622003
MSC: Primary 57; 53; 37;

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.

• Chapters
• 1. Introduction
• 2. Complete affine flows
• 3. Luxuriant foliations
• 4. SL-flows
• 5. SA-flows
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Volume: 1622003
MSC: Primary 57; 53; 37;

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 $SL(2,\mathbb{R})\ltimes \mathbb{R}$.