Secondary Characteristics Classes for Normal Surfaces Singularities

Explore a 43-minute lecture on secondary characteristics classes for normal surfaces singularities delivered by José Luis Cisneros-Molina from the Institute of Mathematics, UNAM. Delve into the concept of Cheeger-Chern-Simons classes as secondary characteristic classes of vector bundles over smooth manifolds with flat connections, defined through differential characters. Learn how these invariants apply to studying normal surface singularities through three main areas: examining topologically trivial representations in compact oriented 3-manifolds using the Index Theorem for flat bundles, understanding the connection to algebraic K-theory, and discovering applications to open problems including the relationship between secondary characteristics classes and spectrum to Klenian singularities. Master the use of these invariants in completing the classification of maximal Cohen-Macaulay modules over quotient surface singularities.