A remark on the Bott class
type: Item
instance of: scholarly article
title: A remark on the Bott class
zbMATH Open document ID: 1008.57021
author: Taro Asuke
published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
publication date: 2003-03-31T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/73542
review text: In several real and complex situations the geometric properties of the characteristic classes of foliations are not yet clear. The author considers the imaginary part \(\xi _q\) of the Bott class. An associated cocycle for \(\xi _q\) in the Čech-de Rham complex is defined. The class \(\xi _q\) reflects how the local holonomy maps expand and rotate transverse discs. The vanishing of this class for foliations having a transverse volume form, or for transversely complex affine foliations, is given. The author shows also that the class \(\xi _q\) has a certain relationship with a group cocycle.
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 57R20
zbMATH DE Number: 1796101
zbMATH Keywords: transversely complex affine foliations
zbMATH Keywords: characteristic classes
reviewed by: Jesus Muciño Raymundo
MaRDI profile type: Publication
OpenAlex ID: W2331052281
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DOI: 10.5802/AFST.981
description: scientific article; zbMATH DE number 1796101