Invariance Theory: The Heat Equation and the Atiyah-Singer Index Theorem

This Book Treats The Atiyah-singer Index Theorem Using The Heat Equation, Which Gives A Local Formula For The Index Of Any Elliptic Complex. Heat Equation Methods Are Also Used To Discuss Lefschetz Fixed Point Formulas, The Gauss-bonnet Theorem For A Manifold With Smooth Boundary, And The Geometrical Theorem For A Manifold With Smooth Boundary. The Author Uses Invariance Theory To Identify The Integrand Of The Index Theorem For Classical Elliptic Complexes With The Invariants Of The Heat Equation.