In the spirit of writing some sort of introductory posts to the things related to what I’m about to spend several years thinking and writing about, I thought I’d try to make a (more or less) layman friendly introduction to Homology and Homotopy.
It’s all residing in the realm of Topology. Topology is the field of mathematics, where those aspects of a shape not dependent on distances are studied. Thus rigidity is not interesting, whereas connectivity is. Narrow/thick is not interesting, but what kind of holes the surface has is. The ultimate thing to be said in topology about two objects is that they are homeomorphic, which technically means that there is an isomorphism between the objects in the category of topological spaces; and more comprehensibly means that there are continuous functions between the shapes such that they are each others inverses.