INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
9783319001289
NATIONAL BIBLIOGRAPHY NUMBER
Country Code
IR
Number
EN-52282
LANGUAGE OF THE ITEM
.Language of Text, Soundtrack etc
انگلیسی
COUNTRY OF PUBLICATION OR PRODUCTlON
Country of publication
IR
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
Hypoelliptic Laplacian and Bott-Chern Cohomolog
General Material Designation
[Book]
Other Title Information
:A Theorem of Riemann-Roch-Grothendieck in Complex Geometry
First Statement of Responsibility
/ by Jean-Michel Bismut
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Heidelberg
Name of Publisher, Distributor, etc.
: Springer International Publishing :Imprint: Birkh?nuser,
Date of Publication, Distribution, etc.
, 2013.
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
XV, 203 p. 1 illus. in color., online resource.
SERIES
Series Title
(Progress in Mathematics
Volume Designation
; 305)
NOTES PERTAINING TO PUBLICATION, DISTRIBUTION, ETC.
Text of Note
Electronic
CONTENTS NOTE
Text of Note
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 cohomology. When the manifolds are K?nhler, our main result is known. A proof can be given using the elliptic Hodge theory of the fibres, its deformation via Quillen's superconnections, and a version in families of the 'fantastic cancellations' of McKean-Singer in local index theory. In the general case, this approach breaks down because the cancellations do not occur any more.One tool used in the book is a deformation of the Hodge theory of the fibres to a hypoelliptic Hodge theory, in such a way that the relevant cohomological information is preserved, and 'fantastic cancellations' do occur for the deformation. The deformed hypoelliptic Laplacian acts on the total space of the relative tangent bundle of the fibres. While the original hypoelliptic Laplacian discovered by the author can be described in terms of the harmonic oscillator along the tangent bundle and of the geodesic flow, here, the harmonic oscillator has to be replaced by a quartic oscillator.Another idea developed in the book is that while classical elliptic Hodge theory is based on the Hermitian product on forms, the hypoelliptic theory involves a Hermitian pairing which is a mild modification of intersection pairing. Probabilistic considerations play an important role, either as a motivation of some constructions, or in the proofs themselves.
Text of Note
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. .?╗╣
SERIES
Title
Progress in Mathematics
Volume Number
305
TOPICAL NAME USED AS SUBJECT
Mathematics
K-theory
Global analysis
Differential equations, partial
Electronic books
LIBRARY OF CONGRESS CLASSIFICATION
Class number
E-BOOK
PERSONAL NAME - PRIMARY RESPONSIBILITY
Bismut, Jean-Michel.
PERSONAL NAME - SECONDARY RESPONSIBILITY
SpringerLink (Online service)
ORIGINATING SOURCE
Country
ایران
ELECTRONIC LOCATION AND ACCESS
Host name
9783319001272.pdf
Access number
عادی
Compression information
عادی
Date and Hour of Consultation and Access
9783319001272.pdf
Electronic Format Type
متن
old catalog
e
BL
1
a
Y
