A higher index theorem for foliated manifolds with boundary

2007/01/17 by Zadeh, Mostafa Esfahani
#53C12 #58J22 #Differential Geometry (math.DG) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.math/0701482

Abstract

Following Gorokhovsky and Lott and using an extension of the b-pseudodifferential calculus of Melrose, we give a formula for the Chern character of the Dirac index class of a longitudinal Dirac type operators on a foliated manifold with boundary. For this purpose we use the Bismut local index formula in the context of non commutative geometry. This paper uses heavily the methods and technical results developed by E.Leichtnam and P.Piazza.

Related

• Index theorey and Non-Commutative Geometry. II. Dirac operators and index bundles
• Index formulae for mixed boundary conditions on manifolds with corners
• Eta cocycles
• Dirac operators on noncommutative manifolds with boundary
• Pseudodifferential operators on manifolds with foliated boundaries