Hypoelliptic Laplacian and Bott<U+0013>Chern Cohomology A Theorem of Riemann<U+0013>Roch<U+0013>Grothendieck in Complex Geometry /

• Main Author: Bismut, Jean-Michel. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Heidelberg : Springer International Publishing : Imprint: Birkhũser, 2013.
• Series: Progress in Mathematics ; 305
• Subjects: Mathematics.; K-theory.; Global analysis.; Differential equations, partial.; K-Theory.; Partial Differential Equations.; Global Analysis and Analysis on Manifolds.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-319-00128-9

The book provides the proof of a complex geometric version of a well-known result in algebraic geometry: the theorem of Riemann<U+0013>Roch<U+0013>Grothendieck for proper submersions. It gives an equality of cohomology classes in Bott<U+0013>Chern cohomology, which is a refinement...

Table of Contents:

• Introduction
• 1 The Riemannian adiabatic limit
• 2 The holomorphic adiabatic limit
• 3 The elliptic superconnections
• 4 The elliptic superconnection forms
• 5 The elliptic superconnections forms
• 6 The hypoelliptic superconnections
• 7 The hypoelliptic superconnection forms
• 8 The hypoelliptic superconnection forms of vector bundles
• 9 The hypoelliptic superconnection forms
• 10 The exotic superconnection forms of a vector bundle
• 11 Exotic superconnections and Riemann<U+0013>Roch<U+0013>Grothendieck
• Bibliography
• Subject Index
• Index of Notation. .