# Tagged Questions

Differential geometry is the application of differential calculus in the setting of smooth manifolds (curves, surfaces and higher dimensional examples). Modern differential geometry focuses "geometric structures" on such manifolds, such as bundles and connections; for questions not concerning such ...

111 views

### Is Floer homology always isomorphic to the singular homology of some space?

After I studied Morse homology, I'm now studying the following Floer homology theories : 1) Symplectic Floer homology ; 2) Floer homology of lagrangians ; 3) Heegard-Floer homology ; ...
44 views

### A book on Vector Calculus with emphasis on geometrical intuition

I am a physicist trying to learn vector calculus in a way that is a mixture of the way mathematicians learn it with the way that physicist learn it in order to be able to learn Differential Geometry ...
39 views

### convention of a default atlas

Recently, I have been studying the basics of differential geometry and te necessary preliminaries. I arrived at the construction of differential structure on topological manifolds, where the non-...
32 views

### smooth manifolds, equivalent statements

Let $X,Y$ be smooth manifolds. Show: A function $f:X\to Y$ is smooth, iff for every open $V\subseteq Y$ and every smooth function $g:V\to\mathbb{R}$ the composition $g\circ f: f^{-1}(V)\to\mathbb{R}$ ...
27 views

### covering space, smooth manifold

Let $p:Y\to X$ be a covering space and $p^{-1}(x)$ countable for every $x\in X$. Task: Let $X$ be a smooth manifold. Show, that $Y$ has the structure of a smooth manifold, regarding this $p$ is ...
31 views

24 views

### Roadmap to Differential Geometry for Machine Learning

Recently within machine learning, there are a lot of works on non-convex optimization and natural gradients methods etc which are based on differential geometry, it gives rise to increased need to ...