Hypoelliptic Laplacian and Orbital Integrals (Annals of Mathematics Studies, Vol. 177) by Jean-Michel Bismut
English | ISBN: 069115130X, 0691151296 | 2011 | 320 pages | PDF | 1,7 MB
This book uses the hypoelliptic Laplacian to evaluate semisimple orbital integrals in a formalism that unifies index theory and the trace formula. The hypoelliptic Laplacian is a family of operators that is supposed to interpolate between the ordinary Laplacian and the geodesic flow. It is essentially the weighted sum of a harmonic oscillator along the fiber of the tangent bundle, and of the generator of the geodesic flow.