Hypoelliptic Laplacian and Bott–Chern Cohomology A Theorem of Riemann–Roch–Grothendieck in Complex Geometry /

• Κύριος συγγραφέας: Bismut, Jean-Michel (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Heidelberg : Springer International Publishing : Imprint: Birkhäuser, 2013.
• Σειρά: Progress in Mathematics ; 305
• Θέματα: Mathematics.; K-theory.; Global analysis (Mathematics).; Manifolds (Mathematics).; Partial differential equations.; K-Theory.; Partial Differential Equations.; Global Analysis and Analysis on Manifolds.

The book provides the proof of a complex geometric version of a well-known result in algebraic geometry: the theorem of Riemann–Roch–Grothendieck for proper submersions. It gives an equality of cohomology classes in Bott–Chern cohomology, which is a refinement for complex manifolds of de Rham cohomo...

Πίνακας περιεχομένων:

• 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–Roch–Grothendieck
• Bibliography
• Subject Index
• Index of Notation.  .