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