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Geometry and topology of three-manifolds

By William Thurston

Electronic version 1.1 - March 2002 - with an index!

This is an electronic edition of the 1980 lecture notes distributed by Princeton University. The text was typed in TeX by Sheila Newbery, who also scanned the figures. Typos have been corrected (and probably others introduced), but otherwise no attempt has been made to update the contents. Genevieve Walsh compiled the index.

Numbers on the right margin correspond to the original edition's page numbers.

Thurston's Three-Dimensional Geometry and Topology, Volume 1 (Princeton University Press, 1997) is a considerable expansion of the first few chapters of these notes. Later chapters have not yet appeared in book form.

Please help improve this document by sending to Silvio Levy at levy@msp.org any useful information such as

  • reports of typos, omissions, and departures from the printed notes that are not purely stylistic
  • references for results attributed without citation
  • references to solutions of then-open problems

A list of errata is here.

File formats

PDFIf you can read and print PDF, you should download the files in this format
PSPostscript files, which can take a long time to print on some printers
PS.GZPostscript files compressed with gzip
ZIPPostscript files compressed with zip
TGZCompressed archive files containing a DVI file and Postscript files for individual figures


I've broken it down into chapters or portions about 20 pages long.

Chapters 10 and 12 don't exist.

(An earlier set of PDF files was kindly prepared and contributed by David Bayer.)

Chapter 1) Geometry and three-manifolds (with front page, introduction, and table of contents), i–vii, 1–7
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Chapter 2) Elliptic and hyperbolic geometry, 9–26
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Chapter 3) Geometric structures on manifolds, 27–43
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Chapter 4) Hyperbolic Dehn surgery, 45–83
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Chapter 5) Flexibility and rigidity of geometric structures, 85–121
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Chapter 6) Gromov's invariant and the volume of a hyperbolic manifold, 123–155
PDF   ( 123–141:  PS   PS.GZ   ZIP   TGZ )   ( 142–155:  PS   PS.GZ   ZIP   TGZ )  

Chapter 7) Computation of volume, by J. W. Milnor, 157–170
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Chapter 8) Kleinian groups, 171–223
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Chapter 9) Algebraic convergence, 225–282
PDF   ( 225–243:  PS   PS.GZ   ZIP   TGZ )   ( 244–263:  PS   PS.GZ   ZIP   TGZ )   ( 263–282:  PS   PS.GZ   ZIP   TGZ )  

Chapter 11) Deforming Kleinian manifolds by homeomorphisms of the sphere at infinity (with a note), 283–295
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Chapter 13) Orbifolds, 297–355
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Index, 357–360
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Complete book   PDF