Let be a smooth map between two manifolds. We call a regular point provided the derivative is non singular, so that there exists a neighbourhood of such that it is diffeomorphically mapped onto its image.(See Inverse function theorem) A point is called a regular value if contains only regular points. Otherwise we call them crtitical […]
Category: Geometry
Differentiable structures-II
In the previous post we have defined a differentiable structure.The definition allows us to talk of differentiable functions i.e., we gave meaning to the term ” f is differentiable function on the manifold”. So basically, differentiable structure is the topological manifold together with sets of differentiable functions where the sets satisfy some properties. For instance […]
Differentiable structures
I am taking a course on differential topology this semester and will be writing a series of posts on this topic. In this post, we will look at the notion of differentiable structures on a topological manifold. The foundational concepts of calculus, including differentiation, tangent vectors, and integration, are robustly defined within the familiar framework […]
A Neighbourhood Of Infinity 