Introduction to topology

The Universal Coefficient Theorem and Quantum Field Theory

“…For the missing proofs of some theorems or lemmas the reader should consult [252] as well as [113], [114]. Loosely speaking, algebraic topology is a systematic way of searching for holes in manifolds and of measuring the properties of various shapes.…”

“…It is important to note that topology does not stand alone [113]. It strongly interferes with geometry and through it with analysis [114]. In order to explain this connection I will discuss a set of results, starting with the standard Riemann-Roch Theorems [115] and going to the results of Grothendieck [116] and Atiyah-Singer [117].…”