Hypoelliptic Laplacian and BottChern Cohomology

Name: Hypoelliptic Laplacian and BottChern Cohomology
Brand: Springer Nature
SKU: 9783319001272
Availability: InStock

Hypoelliptic Laplacian and BottChern Cohomology

Brand

Springer Nature

Manufacturer

N/A

Part Number

GTIN

9783319001272

Condition

New

0 Reviews

0 Questions | 0 Answers

Product Description

The book provides the proof of a complex geometric version of a well-known result in algebraic geometry: the theorem of RiemannRochGrothendieck for proper submersions. It gives an equality of cohomology classes in BottChern cohomology, which is a refinement for complex manifolds of de Rham cohomology. When the manifolds are Khler, 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 McKeanSinger 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.

Available Colors

N/A

Available Sizes

N/A

1 Offer Price Range: $69.99 - $69.99

BEST PRICE

Single Product Purchase

$69.99

@ Link.springer.com BUY Now

Price Comparison

Seller	Contact Seller	List Price	On Sale	Shipping	Best Promo	Final Price	Volume Discount	Financing	Availability	Seller's Page
BEST PRICE 1 Product Purchase @ Link.springer.com Rate Seller This functionality is for registered users only. Go to Login/Register		$69.99	$69.99			$69.99		See Site	In stock	Visit Store