Foliations and the Geometry of 3-Manifolds by Danny Calegari
Foliations and the Geometry of 3-Manifolds - Table of Contents
1. Surface bundles
2. The topology of S¹
3. Minimal surfaces
4. Taut foliations
5. Finite depth foliations
6. Essential laminations
7. Universal circles
8. Constructing transverse laminations
9. Slitherings and other foliations
10. Peano curves
What You Will Learn in Foliations and the Geometry of 3-Manifolds
"Foliations and the Geometry of 3-Manifolds" by Danny Calegari is a comprehensive study of "foliations", "3-manifolds", and their rich interactions with "geometry" and "topology". The book introduces the theory of foliations—decompositions of manifolds into surfaces—and explains how these structures reveal deep properties of three-dimensional spaces. Calegari provides clear exposition on foundational concepts while connecting them to advanced topics in low-dimensional topology.
A central theme of the book is the study of "taut foliations", finite-depth foliations, and essential laminations. It explores how foliations relate to surface bundles, pseudo-Anosov flows, and Thurston’s work on surface automorphisms. Through these ideas, readers gain insight into how dynamic, geometric, and topological structures coexist in 3-manifolds, providing a unified view of complex interactions.
This text is aimed at graduate students and researchers seeking to understand modern developments in 3-manifold theory. By combining rigorous theory with illustrative examples, it serves both as a reference and a guide to current research directions. "Foliations and the Geometry of 3-Manifolds" is essential for anyone studying "low-dimensional topology", "manifold theory", or geometric structures in mathematics.
Book Details & Specifications
Title:
Foliations and the Geometry of 3-Manifolds by Danny Calegari
Publisher:
Clarendon Press
Year:
2007
Pages:
371
Type:
PDF
Language:
English
ISBN-10 #:
B001CXO104
ISBN-13 #:
978-0191524639
License:
External Educational Resource
Amazon:
Amazon
About the Author: Danny Calegari
The author
Danny Calegari
is an "Australian-American mathematician" and Professor at the "University of Chicago", is known for his work in "low-dimensional topology" and dynamical systems. His research combines rigorous mathematics with geometric intuition, making this book a valuable resource for understanding the rich structure and dynamics of three-dimensional manifolds. His work is a detailed exploration of "3-manifold topology", "foliations", and "geometric structures". The book introduces advanced concepts such as taut foliations, laminations, and hyperbolic geometry, making complex ideas accessible to graduate students and researchers in modern "geometric topology".
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