Cappell-Miller analytic torsion for manifolds with boundary

Huang, Rung Tzung

doi:10.1090/s0002-9939-10-10362-1

Cited by 3 publications

(2 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [15], Huang also defined the Cappell-Miller analytic torsion on manifolds with boundary using the max/min extension and get the anomaly formula in the case of the family of metrics are fixed near the boundary.…”

Section: )mentioning

confidence: 99%

A Cheeger–Müller theorem for Cappell–Miller torsions on manifolds with boundary

2015

manuscripta math.

View full text Add to dashboard Cite

In this paper, we extend the Cappell-Miller analytic torsion to manifolds with boundary under the absolute and relative boundary conditions and using the techniques of Brüning-Ma and Su-Zhang, we get the anomaly formula of it for odd dimensional manifolds. Then by the methods of Brüning-Ma, Cappell-Miller and Su-Zhang, we get the CheegerMüller theorem for the Cappell-Miller analytic torsion on odd dimensional manifolds with boundary up to a sign. As a consequence of the main theorem, we get the gluing formula for the Cappell-Miller analytic torsion which generalizes a theorem of Huang.

show abstract

Section: )mentioning

confidence: 99%

A Cheeger–Müller theorem for Cappell–Miller torsions on manifolds with boundary

2015

manuscripta math.

View full text Add to dashboard Cite

show abstract

“…Cappell and Miller used non-selfadjoint Laplace operator to define another complex valued analytic torsion and proved the extension of the Cheeger-Müller theorem ( [10]), which we call the Cappell-Miller analytic torsion. Inspired by the result of B. Vertman, G. Su ( [30]) and the first author ( [18]) studied the Burghelea-Haller analytic torsion and the Cappell-Miller analytic torsion, respectively, on a compact oriented Riemannian manifolds with boundary. O. M. Molina ([25]) discussed the Burghelea-Haller analytic torsion on a compact Riemannian manifold with boundary by using the relative/absolute boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

The refined analytic torsion and a well-posed boundary condition for the odd signature operator

Huang

Lee

2018

Journal of Geometry and Physics

Self Cite

View full text Add to dashboard Cite

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 B in the sense of Seeley. We then show that the zeta-determinants of B 2 and eta-invariants of B 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.

show abstract

The refined analytic torsion and a well-posed boundary condition for the odd signature operator

Huang¹,

Lee²

2010

Preprint

View full text Add to dashboard Cite

Cappell-Miller analytic torsion for manifolds with boundary

Cited by 3 publications

References 25 publications

A Cheeger–Müller theorem for Cappell–Miller torsions on manifolds with boundary

A Cheeger–Müller theorem for Cappell–Miller torsions on manifolds with boundary

The refined analytic torsion and a well-posed boundary condition for the odd signature operator

The refined analytic torsion and a well-posed boundary condition for the odd signature operator

Contact Info

Product

Resources

About