Program
Triangulations and combinatorial differential geometry
Student No.:50
Time:Mon/Wed 15:10-17:00, 2014-07-07 ~ 2014-07-16
Instructor:Stephan Tillmann  [The University of Sydney]
Place:Conference Room 4, Floor 2, Jin Chun Yuan West Building
Starting Date:2014-7-7
Ending Date:2014-7-16

 

 

Description:

 

The theme of this course is connections between combinatorics and geometry in the study of triangulated manifolds. I will describe various geometric properties that can be computed from triangulations, and connections (or obstructions) between them and the combinatorics of a triangulation. The starting point will be triangulations and ideal triangulations of 3-dimensional manifolds, such as knot complements. I will describe how various geometric structures (e.g. hyperbolic, Cauchy-Riemann and Anti-de-Sitter) can be computed from triangulations, and how normal surface theory leads to natural obstructions. Moreover, moduli spaces of such structures will be studied viainteresting functions on them.In arbitrary dimensions, I will focus onCAT(0) structures and discrete notions of spin structures computed from triangulations.

 

 
 

Prerequisite:

 

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

 

 
 

Reference:

 
Lecture notes and additional materials will be made available during the course.