Predavatelj: Zoran Škoda (Sveučilište u Zagrebu)

By a construction of H. Cartan, a simplicial analogue of principal bundles, with simplicial group as the structure group, can be constructed as a twisted analogue of cartesian product
of the simplicial group and base simplicial set. The datum used for the twisting is the Cartan’s twisting function. Principal bundles are classified by the first nonabelian cohomology and can
carry connections in the sense of differential geometry. Higher nonabelian cocycles appear in many modern applications in geometry, topology, operator algebras and mathematical physics.
Using pseudosimplicial categories instead of simplicial sets we can categorify Cartan’s construction. After general introduction to the classical twisting function and modern motivation for higher cocycles, I will present a sketch of the categorification of twisting function in a joint work in progress with B. Jurčo. The coherences are rather elaborate, as we have calculated on the basis of Jardine’s supercoherence, hence they seem rather not practical for calculation. However, we expect to use them to aid a construction and further study of the expected categorification of universal simplicial principal bundle (classically obtained using delooping functor W bar of the simplicial group) in the pseudosimplicial language.

Predavanje bo na FNM, Koroška cesta 160, v predavalnici 0/103.