Secondary Characteristics Classes for Normal Surfaces Singularities - Part 2

Learn about Cheeger-Chern-Simons secondary characteristic classes and their applications to normal surface singularities in this 49-minute mathematics lecture from the Institute of Mathematics, UNAM. Explore how these classes, defined using differential characters for vector bundles with flat connections over smooth manifolds, generate new insights into surface singularity analysis. Discover the computation methods for these classes on compact oriented 3-manifolds using the Atiyah-Patodi-Singer Index Theorem, with special focus on rational homology spheres. Examine the natural connections to algebraic K-theory and understand practical applications including relationships to Klenian singularities' spectrum and the classification of maximal Cohen-Macaulay modules over quotient surface singularities.