|Operator invariants of 3-manifolds with PSL(2,C)-characters|
|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|
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