Operator invariants of 3-manifolds with PSL(2,C)-characters
Student No.:50
Time:Wed. 15:10-17:00; Fri. 10:10-12:00 (Last lecture on Apr. 23: 10:10-12:00)
Instructor:Stéphane Baseilhac  [Université Montpellier 2]
Place:Conference Room 3, Floor 2, Jin Chun Yuan West Building
Starting Date:2012-4-6
Ending Date:2012-4-23

Course description:

This course will complement the courses given by Professors Luo and Segerman. We will describe the simplicial formulation of Chern-Simons theory for 3-manifolds with PSL(2,C)-characters. For cusped hyperbolic 3-manifolds Chern-Simons theory can be (almost) identified with a complexified volume function on the deformation variety. In particular we will introduce and use Neumann's extended Bloch group and a refinement of the gluing equations to obtain a calculus for triangulations realizing classes in the discrete homology group H_3(PSL(2,C);Z). Such a calculus will lead us to the construction of the quantum hyperbolic invariants of cusped hyperbolic 3-manifolds, which make a non commutative deformation of Chern-Simons invariants based on the representation theory of the quantum group Uqsl(2).



Some knowledge of algebraic topology and hyperbolic geometry would be helpful.


Reference for the course:

S. Baseilhac, R. Benedetti, Classical and quantum dilogarithmic invariants of flat PSL(2,C)-bundles over 3-manifolds, Geom. Topol. 9 (2005) 493-570

W.D. Neumann, Extended Bloch group and the Cheeger-Chern-Simons class, Geom. Topol. 8 (2004) 413-474