2019/03/27 by Mohsen, Omar
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1903.11583
We express Witten's deformation of Morse functions using deformation to the normal cone and C^*-modules. This allows us to obtain asymptotics of the `large eigenvalues'. Our methods extend to Morse functions along a foliation. We construct the Witten deformation using any generic function on an arbitrary foliation on a compact manifold and establish the compactness of its resolvent. When the foliation has a holonomy invariant transverse measure we show that our result implies Morse inequalities obtained by Connes and Fack in a slightly more general situation.