Program
Introduction to Teichmuller space of surfaces and hyperbolic 3-manifolds
Student No.:50
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
Starting Date:2013-5-10
Ending Date:2013-6-13

 

Description:

 

 

 

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

 

 

 

 

Prerequisite:

The students should know some basic algebraic topology (fundamental groups, covering spaces) and Riemannian geometry.

 

Reference:

 

 

 

[1] Peter Buser: Geometry and spectra of compact Riemann surfaces, Birkauser 1992.

[2] Riccardo Benedetti, Carlo Petronio, Lectures on Hyperbolic Geometry, Springer, 2003

[3] W. Thurston, Topology and Geometry of 3-manifolds, http://library.msri.org/books/gt3m/