Essential manifolds
Definition of essential manifolds, lens spaces as example of non-aspherical essential manifolds.
Tag: manifold
Aspherical manifolds
Aspherical manifolds, Eilenberg-MacLane spaces, classifying spaces of groups via the nerve construction.
A manifold whose functions are the smooth functions on the real line with rational period
A solution to exercises 3.17.4, 3.17.5, 3.9.5, 3.28.3 in Jet Nestruev: "Smooth Manifolds and Observables", Springer, 2003 and similar problems, along explanations.
Classifying Riemann surfaces
I sketch a (well-known) classification of Riemann surfaces. I wrote this because I couldn't find a quick overview of the classification on the web. References for further reading in the wikipedia are given in the text.
