Higher Math: Geometry and Topology
Read this topicExplanations 3
- Riemannian and esp. hyperbolic geometry in Sarnak course... e.g. Laplacian of hyperbolic spaces used early. Terry Tao 285G, Lecture 0: Riemannian manifolds and curvature... want…
By Victor Wang
- Sheaves of differentials Nice to have different perspectives. See even Neukirch for "arithmetic Riemann-Roch theory" (including a notion of genus of number field, and so on). Wa…
By Victor Wang
- Frobenius' theorem on vector fields (more precisely, on integrable subbundles of the tangent bundle) A good high-level perspective I like is at MSE: Wanted: A purely algebraic p…
By Victor Wang
Problems 4
- Can you cover the real plane, R2\mathbb{R}^2R2, using a disjoint set of topological T's? \\ [Source: Communicated by Mark Sellke, and separately by David (Ting-Chun) Lin, who he…
- Let f :R2→Rf\colon \mathbb{R}^2\to \mathbb{R}f:R2→R be smooth, with (0,0)(0,0)(0,0) a local minimum and the unique critical point of fff. Need it be a global minimum? \\ [Sourc…
- Can you cover the real plane, R2\mathbb{R}^2R2, using a disjoint set of topological O's? \\ [Source: Classical?]
- On the other hand, there is an inclusion ι\iotaι of C∗\mathbb{C}^\astC∗ into GLnC\operatorname{GL}_n \mathbb{C}GLnC (the diagonal matrix embedding z↦z⋅Inz\mapsto z\cdot I_nz↦z…