I have a strong understanding of Representation Theory but am interested in learning from Voisin, Hodge Theory and Complex Algebraic Geometry. What are the prerequisites to learning from this ...
How much has been the group of diffeomorphisms of a manifold " been studied. I got this information from wiki. " Quite a lot is known about the group of diffeomorphisms of the circle. Its Lie algebra ...
In wikipedia,I was pretty amazed to find a proof of fundamental theorem of algebra using gauss bonnet theorem.I think given how central it is to mathematics with its far reaching generalizations like ...
Based on this mathoverlow question, I would like to have a similar list for the case of string manifolds. An $n$-dim. Riemannian manifold $M$ is said to be string, if the classifying map of its bundle ...
I'm trying to get a grasp on what it means for a manifold to be spin. My question is, roughly: What are some "good" (in the sense of illustrating the concept) examples of manifolds which are spin ...
What are some major open problems in Riemannian Geometry? I tried googling it, but couldn't find any resources.
Do you know properties which distinguish four-dimensional spaces among the others? What makes four-dimensional topological manifolds special? What makes four-dimensional differentiable manifolds ...
In two different books I found these two related statements. The book by Jost defines a ``locally symmetric space" as one for which the curvature tensor is constant and which is geodesically ...
This is not a question, but I just hope to hear more from everyone here on it. A list of ready-to-use machineries to compute the de Rham / Cech cohomology of a manifold / variety. As far as I know, I ...
I have studied differential geometry, and am looking for basic introductory texts on Riemmanian geometry. My target is eventually Kähler geometry, but certain topics like geodesics, curvature, ...
I have often heard in the folk-lore that Feynman Path Integral can be used to compute geometric invariants of a space. Coming from a background of studying Quantum Field Theory from the books like ...