|Speaker:||Kiyonori Gomi (Kyoto University)|
|Title:||Multiplication in differential cohomology and cohomology operation|
|Date (JST):||Mon, Jun 08, 2009, 17:00 - 18:30|
|Place:||Room 002, Mathematical Sciences Building, Komaba Campus|
The notion of differential cohomology refines generalized cohomology theory so as to incorporate information of differential forms. The differential version of the ordinary cohomology has been known as the Cheeger-Simons cohomology or the smooth Deligne cohomology, while the general case was introduced by Hopkins and Singer around 2002.
The theme of my talk is the cohomology operation induced from the squaring map in the differential ordinary cohomology and the differential K-cohomology: I will relate these operations to the Steenrod operation and the Adams operation. I will also explain the roles that the squaring maps play in 5-dimensional Chern-Simons theory for pairs of B-fields and Hamiltonian quantization of generalized abelian gauge fields.