URegina Topology and Geometry Seminar: Yang Hu

At this point we have two cohomology theories in hand – HZ (singular cohomology) and KU (complex K-theory) – and the Chern character ch establishes a comparison between them. Even the first properties of ch can already give rise to interesting consequences, as we saw last time. 
 

The story, however, does not simply stop here. Both HZ and KU are “very geometric”, as they support Thom classes for complex vector bundles. This talk will invite us to take a further (geometric) look at the comparison ch: how does it compare the K-theoretic Thom class with the ordinary cohomological one? Exploring this question will lead us to define the Todd class as the correction term, and to introduce a topological version of the Grothendieck-Riemann-Roch theorem.
 

Additional advertisement for topologists: This talk will open the doors to a number of important future topics, including the e-invariant and the J-homomorphism.
 

Additional advertisement for number theorists: Bernoulli numbers will appear (multiple times) in the talk.