3-dimensional geometry and topology
(2006. 1st semester)

Wednesday 4:00-5:00
Room: 4416

We begin on February 15 and will meet every Wednesday and continue on until the end of the 1st semester of 2006. We might be able to finish the book this semester.

webpage: math.kaist.ac.kr/~schoi/3dim20061.htm

This is an informal seminar studying the above book by William Thurston published by Princeton University Press in 1997, meeting once a week during the fall semester of 2005. We hope to continue these seminars in the winter of 2005 and the fall of 2006 as well. I'll basically give all the talks. The course should be elementary and undergraduates are welcomed to come to the meetings.

The book is now an elementary one covering the introductory part of the original note "Geometry and Topology of 3-manifolds".

Basic plans:
  Introduction to hyperbolic spaces:  using Ratcliffe and Beardon
  Then we will basically follow Thurston's book.
    Topics: Hyperbolic spaces, isometry groups
           Chapter 1: What is a manifold? (This is an introduction)
           Chapter 2: Hyperbolic geometry and its friends (This explains hyperbolic space,
                           isometry, computations on hyperbolic spaces)
           Chapter 3: Geometric manifolds (Defines geometric structures, developing
                           maps, 8 model geometries in 3-dimensional spaces)
           Chapter 4: Structures of Discrete groups (Bieberbach theorem, Euclidean and
                           elliptic manifolds, thick and thin decompositions, Teichmuller
                           space)
If we are very hard working, we may start working on "The geometry and topology of three-manifolds" (http://www.msri.org/publications/books/gt3m/)  

References: 
 
Thurston: Thee-dimensional geometry and topology, Princeton University Press
 
Ratcliffe: Foundations of hyperbolic manifolds, Spinger Verlag
 Beardon: The geometry of discrete groups, Springer Verlag
 Wolf: Spaces of constant curvature, 5th edition, Publish or Perish
 

Since there are many interesting related websites, I will add them here:

Geometry Center: http://www.geom.uiuc.edu
  There is a video introducing the hyperbolic three-space:   http://www.geom.uiuc.edu/graphics/pix/Video_Productions/Not_Knot/
  There are many other resources here: programs, introductory articles, and so on.

Geometry games by J. Weeks:  http://www.geometrygames.org/
    In particular, Snappea is a program to compute hyperbolic structures on 3-manifolds.

Experimental Geometry Lab (University of Maryland):http://egl.math.umd.edu/
   There are nice pictures and programs.

Computop.org softwares: http://www.its.caltech.edu/~dunfield/computop/index.html
    Many research level softwares for 3-dimensional topology

 Knitting and topology: http://www.theiff.org/oexhibits/oe1e.html,
                                  http://cerebro.cs.xu.edu/~smbelcas/math-knit.html