Some Secondary Geometric Invariants
Zhizhang Xie, Vanderbilt University
Location: Stevenson 1432
Secondary invariants are important in geometry and topology. While primary invariants only depend on the topology of the underlining manifolds, secondary invariants also depend on certain auxiliary geometric data (e.g. metrics or connections etc. ) of the underlining manifolds. Some of the well-known secondary invariants are Chern-Simon invariants, eta invariant and rho invariant, where the latter two were introduced by Atiyah, Patodi and Singer. In this talk, I will discuss some of my recent work and joint work with others on these secondary invariants (and their higher versions). In particular, I shall talk about the higher eta invariant and the higher rho invariant, and their connections to the Baum-Connes conjecture and positive scalar curvature problems.