Differential Geometry

Albanese Map of a Riemannian Manifold

2021-02-21 Fei Ye
𝔾iven a compact Riemannian manifold $M$ such that the first Betti number $b$ is nonzero, there exists a map $\operatorname{alb}: M\to \mathbb{R}^b/\mathbb{Z}^b$, called the Albanese map. The aim of post is to prove the smoothness of the Albanese map. Read more →

Coadjoint Orbits

2021-01-12 Fei Ye
ℂoadjoint orbits are examples of symplectic manifolds. This post aims at defining coadjoint orbits with a review on Lie group action. Read more →

A Brief Introduction to Cohomology of Lie Algebra

2021-01-07 Fei Ye
𝕃et $G$ be a compact simply connected Lie group and $\mathfrak{g}$ its Lie algebra. In this posts, we will discuss the motivation of Lie algebra cohomology of $\mathfrak{g}$ and its connection with the de Rham cohomology of $G$. Read more →

Poisson Bivectors

2020-08-03 Fei Ye
𝔼quivalence between Poisson brackets and Poisson bivectors will be studied in this post. Read more →