講演会

過去の記録 ~06/23次回の予定今後の予定 06/24~


2018年07月10日(火)

15:00-16:00   数理科学研究科棟(駒場) 128号室
Sam Nariman 氏 (Northwestern University)
On the moduli space of flat symplectic surface bundles
[ 講演概要 ]
There are at least three different approaches to construct characteristic invariants of flat symplectic bundles. Reznikov generalized Chern-Weil theory for finite dimension Lie groups to the infinite dimensional group of symplectomorphisms. He constructed nontrivial invariants of symplectic bundles whose fibers are diffeomorphic to complex projective spaces. Kontsevich used formal symplectic geometry to build interesting classes that are not yet known to be nontrivial. Also for surface bundles whose holonomy groups preserve the symplectic form, Kotschick and Morita used the flux homomorphism to construct many nontrivial stable classes.

In this talk, we introduce infinite loop spaces whose cohomolgy groups describe the stable characteristic invariants of symplectic flat surface bundles. As an application, we give a homotopy theoretic description of
Kotschick and Morita's classes and prove a result about codimension 2 foliations that implies the nontriviality of KM classes.