Hello there! Topological insulators and supercontuctors nowadays are very active field in physic research. I am looking for a Phd in theoretical matter physics, and these arguments could interest me. But I have a question: phisicists that study topological superconductors, insulators and similar know topology almost 'as a matematician'? They study topology in deep manner? Or this word is used as in the feynmann diagram for example, in which one says that two diagrams give a different contribution if they are topologically distinct (but without a deep mathematic meaning of the word 'topology').