1-forms over the moduli space of irreducible connections defined by the spectrum of Dirac operators
type: Item
instance of: scholarly article
title: 1-forms over the moduli space of irreducible connections defined by the spectrum of Dirac operators
zbMATH Open document ID: 0666.53015
DOI: 10.1016/0393-0440(87)90005-2
author: Helga Baum
published in: Journal of Geometry and Physics
publication date: 1987-01-01T00:00:00Z
review text: The author defines a sequence of 1-forms \(a_ f^{(k)}\) on the moduli space of irreducible connections on a principal bundle over a Riemannian manifold M depending on a function f on M. If A(u) is a path of connections in the moduli space the author defines \(T_{\omega}=d/du(D_{A(u)}-f)|_{u=0},\) where \(\omega\) is the tangent vector to the path. Then the one forms are the coefficients in the asymptotic expansion of trace \((T_{\omega}\exp (-t(D_ A-f)^ 2)).\) The author calculates these one-forms for the cases \(k=0,1,2\), relates them to the \(\eta\)-function of the Dirac operator and studies other of their properties.
Mathematics Subject Classification ID: 53C05
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 58J35
zbMATH DE Number: 4090285
zbMATH Keywords: moduli space of irreducible connections
zbMATH Keywords: principal bundle
zbMATH Keywords: asymptotic expansion
zbMATH Keywords: Dirac operator
reviewed by: Michael K. Murray
MaRDI profile type: Publication
full work available at URL: 0393-0440(87)90005-2
OpenAlex ID: W2066861974
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description: scientific article; zbMATH DE number 4090285