Topology and Combinatorics of 3-Manifolds

1995
ISBN: 978-3-540-59063-7
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1599, 450 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1440 g

Reihe: Lecture Notes in Mathematics

This book is a study of combinatorial structures of 3-mani- folds, especially Haken 3-manifolds. Specifically, it is concerned with Heegard graphs in Haken 3-manifolds, i.e., with graphs whose complements have a free fundamental group. These graphs always exist. They fix not only a combinatorial stucture but also a presentation for the fundamental group of the underlying 3-manifold. The starting point of the book is the result that the intersection of Heegard graphs with incompressible surfaces, or hierarchies of such surfaces, is very rigid. A number of finiteness results lead up to a ri- gidity theorem for Heegard graphs. The book is intended for graduate students and researchers in low-dimensional topolo- gy as well as combinatorial theory. It is self-contained and requires only a basic knowledge of the theory of 3-manifolds

Zielgruppe

Research

Autoren/Hrsg.

Johannson, Klaus

Fachgebiete

• Mathematik | Informatik Mathematik Operations Research Graphentheorie
• Mathematik | Informatik Mathematik Algebra
• Mathematik | Informatik Mathematik Topologie

Inhaltsverzeichnis

Handlebodies.- Relative handlebodies.- Generalized one-relator 3-manifolds.- N-relaton 3-manifolds.- The space of heegaard graphs.