Cell complexes are spaces made of pieces which are part of Euclidean space, generalizing polyhedra. These are the most classic spaces on which groups of transformations act. This is also the setting for knot theory. History See the article on Topology at St Andrews. There is however some semblance to the present topic among metric spaces .
Simplicial complexes are essentially polyhedra .
Problems specific to Euclidean space may be treated in the geometry pages Questions regarding, say, smoothness on balls and spheres are in the FAQ for spheres . Many now-classical results date from that period. In particular, it analyzes the hyperbolic structure of knot complements. Here are the AMS and Goettingen resource pages for area 57. Deriving the equations of a torus .