Rung-Tzung Huang

THE REFINED ANALYTIC TORSION AND A WELL-POSED BOUNDARY CONDITION FOR THE ODD SIGNATURE OPERATOR

In this paper we discuss the refined analytic torsion on an odd dimensional compact oriented Riemannian manifold with boundary under some assumption. For this purpose we introduce two boundary conditions which are complementary to each other and well-posed for the odd signature operator

Cappell-Miller analytic torsion for manifolds with boundary

\mathcal{B}

The Anomaly Formula of the Analytic Torsion on CR Manifolds with S^1 action

in the sense of Seeley. We then show that the zeta-determinants of

Refined analytic torsion: comparison theorems and examples

\mathcal{B}^2

The gluing formula of the refined analytic torsion for an acyclic Hermitian connection

and eta-invariants of

The comparison of two constructions of the refined analytic torsion on compact manifolds with boundary

\mathcal{B}

Refined analytic torsion for twisted de Rham complexes

subject to these boundary conditions are well defined by using the method of the asymptotic expansions of the traces of the heat kernels. We use these facts to define the refined analytic torsion on a compact manifold with boundary and show that it is invariant on the change of metrics in the interior of the manifold. We finally describe the refined analytic torsion under these boundary conditions as an element of the determinant line.

TWISTED CAPPELL―MILLER HOLOMORPHIC AND ANALYTIC TORSIONS

Inspired by the work of Boris Vertman on refined analytic torsion for manifolds with boundary, in this paper we extend the construction of the Cappell-Miller analytic torsion to manifolds with boundary. We also compare it with the refined analytic torsion on manifolds with boundary. As a byproduct of the gluing formula for refined analytic torsion and the comparison theorem for the Cappell-Miller analytic torsion and the refined analytic torsion, we establish the gluing formula for the Cappell-Miller analytic torsion in the case where the Hermitian metric is flat.

Morse inequalities for Fourier components of Kohn-Rossi cohomology of CR covering manifolds with

Let

S^1

X