|Introduction to Teichmuller space of surfaces and hyperbolic 3-manifolds|
|Time：||The lecture on June 11 is NOT canceled (First meeting 2013-05-10 10:10-12:00) Tue/Thu 10:10-12:00|
|Instructor：||Feng Luo [Rutgers University]|
|Place：||Conference Room 1, Floor 1, Jin Chun Yuan West Building|
This is an introduction course for undergraduate and graduate students who are interested on low-dimensional geometry and topology. Due to the uniformization theorem of surfaces and geometrization conjecture for 3-manifolds, we will use hyperbolic geometry as the basic tool. Hyperbolic metrics will be used to understand the Teichmuller space of surfaces and topology of 3-manifolds. The topics to be covered are:
1. Hyperbolic spaces in dimension 2 and 3.
2. Hyperbolic metrics on surfaces: geodesics, Gauss-Bonnet, collar lemmas, Ber’s constant, Wolpert’s cosine law.
3. Teichmuller space of surfaces: Fenchel-Nielsen coordinate
4. Mostow rigidity for hyperbolic metrics on 3-manifolds
5. Gromov norm and Gromov-Thurston’s theorem relating Gromov norm to volume
The students should know some basic algebraic topology (fundamental groups, covering spaces) and Riemannian geometry.
 Peter Buser: Geometry and spectra of compact Riemann surfaces, Birkauser 1992.
 Riccardo Benedetti, Carlo Petronio, Lectures on Hyperbolic Geometry, Springer, 2003
 W. Thurston, Topology and Geometry of 3-manifolds, http://library.msri.org/books/gt3m/