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Hypoelliptic Laplacian and Bott–Chern Cohomology (Record no. 23506)

000 -LEADER
fixed length control field 03748nam a22004455i 4500
003 - CONTROL NUMBER IDENTIFIER
control field OSt
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20140310151453.0
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
fixed length control field cr nn 008mamaa
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 130524s2013 gw | s |||| 0|eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9783319001289
978-3-319-00128-9
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QA612.33
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 512.66
Edition number 23
264 #1 -
-- Heidelberg :
-- Springer International Publishing :
-- Imprint: Birkhäuser,
-- 2013.
912 ## -
-- ZDB-2-SMA
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Bismut, Jean-Michel.
Relator term author.
245 10 - IMMEDIATE SOURCE OF ACQUISITION NOTE
Title Hypoelliptic Laplacian and Bott–Chern Cohomology
Medium [electronic resource] :
Remainder of title A Theorem of Riemann–Roch–Grothendieck in Complex Geometry /
Statement of responsibility, etc by Jean-Michel Bismut.
300 ## - PHYSICAL DESCRIPTION
Extent XV, 203 p. 1 illus. in color.
Other physical details online resource.
440 1# - SERIES STATEMENT/ADDED ENTRY--TITLE
Title Progress in Mathematics ;
Volume number/sequential designation 305
505 0# - FORMATTED CONTENTS NOTE
Formatted contents 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.  .
520 ## - SUMMARY, ETC.
Summary, etc 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 Kähler, 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.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Mathematics.
Topical term or geographic name as entry element K-theory.
Topical term or geographic name as entry element Global analysis.
Topical term or geographic name as entry element Differential equations, partial.
Topical term or geographic name as entry element Mathematics.
Topical term or geographic name as entry element K-Theory.
Topical term or geographic name as entry element Partial Differential Equations.
Topical term or geographic name as entry element Global Analysis and Analysis on Manifolds.
710 2# - ADDED ENTRY--CORPORATE NAME
Corporate name or jurisdiction name as entry element SpringerLink (Online service)
773 0# - HOST ITEM ENTRY
Title Springer eBooks
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Display text Printed edition:
International Standard Book Number 9783319001272
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier http://dx.doi.org/10.1007/978-3-319-00128-9
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Source of classification or shelving scheme
Item type E-Book
Copies
Price effective from Permanent location Date last seen Not for loan Date acquired Source of classification or shelving scheme Koha item type Damaged status Lost status Withdrawn status Current location Full call number
2014-04-10AUM Main Library2014-04-10 2014-04-10 E-Book   AUM Main Library512.66