The geometry and topology of three-manifolds
The geometry and topology of three-manifolds is a set of widely circulated but unpublished notes by William Thurston from 1978 to 1980 describing his work on 3-manifolds. The notes introduced several new ideas into geometric topology, including orbifolds, pleated manifolds, and train tracks.
Distribution
Copies of the original 1980 notes were circulated by Princeton University. Later the Geometry Center at the University of Minnesota sold a loosely bound copy of the notes. In 2002, Sheila Newbery typed the notes in TeX and made a PDF file of the notes available, which can be downloaded from MSRI using the links below. The book (Thurston 1997) is an expanded version of the first three chapters of the notes.
Contents
Chapters 1 to 3 mostly describe basic background material on hyperbolic geometry.
Chapter 4 cover Dehn surgery on hyperbolic manifolds
Chapter 5 covers results related to Mostow's theorem on rigidity
Chapter 6 describes Gromov's invariant and his proof of Mostow's theorem.
Chapter 7 (by Milnor) describes the Lobachevsky function and its applications to computing volumes of hyperbolic 3-manifolds.
Chapter 8 on Kleinian groups introduces Thurston's work on train track and pleated manifolds
Chapter 9 covers convergence of Kleinian groups and hyperbolic manifolds.
Chapter 10 does not exist.
Chapter 11 covers deformations of Kleinian groups.
Chapter 12 does not exist.
Chapter 13 introduces orbifolds.
References
- Canary, R. D.; Epstein, D. B. A.; Green, P. (2006) [1987], "Notes on notes of Thurston", in Canary, Richard D.; Epstein, David; Marden, Albert, Fundamentals of hyperbolic geometry: selected expositions, London Mathematical Society Lecture Note Series, 328, Cambridge University Press, ISBN 978-0-521-61558-7, MR 0903850
- Thurston, William (1980), The geometry and topology of three-manifolds, Princeton lecture notes
- Thurston, William P. (1997), Levy, Silvio, ed., Three-dimensional geometry and topology. Vol. 1, Princeton Mathematical Series, 35, Princeton University Press, ISBN 978-0-691-08304-9, MR 1435975