An analytical proof of the atiyah-singer index theorem for dirac operators

Abstract

"The index of a Fredholm operator acting on a Hilbert space is the integer number defined as the difference between the dimension of its kernel and its cokernel. In some particular cases -such as the geometrical context we consider along this work - this integer number can be computed from integral expressions involving geometrical and topological data from the background space. This is the case of the index for Dirac operators considered in this manusscript, written for a master thesis of the University of Los Andes in Bogotá, Colombia (under the supervision of Sergio Adarve and Alexander Cardona), as an attempt to present an analytical proof of the Atiyah-Singer theorem (AS)¿"--Tomado de la Introducción.