Use of Topology in physical problems
  Some of the basic concepts of topology are explored through known physics problems. This helps us in two ways, one, in motivating the definitions and the concepts, and two, in showing that topological analysis leads to a clearer understanding of the problem. The problems discussed are taken from classical mechanics, quantum mechanics, statistical mechanics, solid state physics, and biology (DNA), to emphasize some unity in diverse areas of physics. It is the real Euclidean space, $R^d$, with which we are most familiar. Intuitions can therefore be sharpened by appealing to the relevant features of this known space, and by using these as simplest examples to illustrate the abstract topological concepts. This is what is done in this chapter. 
Somendra M Bhattacharjee
cond-mat.other cond-mat.stat-mech hep-th