Characteristic Classes implemented in SageMath

22.05. bis 22.05.2019, 4:00 - 4:30 pm  –  Haus 9, Raum 2.22

Michael Jung

SageMath is an open source variant of Mathematica and useful in various areas in mathematics. For my master thesis, I implement characteristic classes of vector bundles using the Chern--Weil homomorphism. Characteristic classes can describe the `twistedness` of a vector bundle and are important ingredients of the Atiyah--Singer index theorem. Given a vector bundle E->M over a differentiable manifold M, it is possible to construct any real (or complex) characteristic class (like the Euler class) out of some connection matrix given on E. In this talk I will shortly introduce characteristic classes and explain the algorithm. If there is some time, I will present a demo notebook of my current progress in SageMath.