Physics Seminar

“An Introduction to Cohomology groups”

Dr. Hyojin Jung

NIMS

Jan. 26th (Tue), 13:00, E6 #1501

Simplicial homology groups of Δ-complexes are quite directly treated as a tool of counting n-dimensional spheres. However, when we consider its dual space called cohomology groups, it's not easy to find geometric meaning intuitively. In this talk, we introduce simplicial cohomology groups of Δ-complexes giving geometric interpretation. Additionally, we show another cohomology groups, the de Rham cohomology groups with the exterior differentiation which is regarded as the extension of gradient, curl, and divergence of vector calculus on R^3. Through these approaches we can improve comprehension of cohomology groups.

Department of Physics, KAIST