1-forms over the moduli space of irreducible connections defined by the spectrum of Dirac operators (Q1116466)

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.