An extension of a theorem by Cheeger and Müller to spaces with isolated conical singularities

Ludwig, Ursula

doi:10.1215/00127094-2020-0008

Duke Math. J.

2020

DOI: 10.1215/00127094-2020-0008

|View full text |Cite

An extension of a theorem by Cheeger and Müller to spaces with isolated conical singularities

Ursula Ludwig¹

Abstract: Differential geometryAn extension of a theorem by Cheeger and Müller to spaces with isolated conical singularities Une extension d'un résultat de Cheeger et Müller pour un espace à singularités coniques isolées

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Analytic Torsion for Fibred Boundary Metrics and Conic Degeneration

Olsen Lye,

Vertman

2024

International Mathematics Research Notices

View full text Add to dashboard Cite

We study the renormalized analytic torsion of complete manifolds with fibred boundary metrics, also referred to as $\phi $-metrics. We establish invariance of the torsion under suitable deformations of the metric, and establish a gluing formula. As an application, we relate the analytic torsions for complete $\phi $- and incomplete wedge-metrics. As a simple consequence we recover a result by Guillarmou and Sher about analytic torsion under conic degeneration.

show abstract

Analytic Torsion for Fibred Boundary Metrics and Conic Degeneration

Olsen Lye,

Vertman

2024

International Mathematics Research Notices

View full text Add to dashboard Cite

show abstract

A Morse-Bott type complex and the Bismut–Zhang torsion for intersection cohomology

Ludwig

2024

Annales De l'Institut Fourier

View full text Add to dashboard Cite

In the first part of this article we establish, for a compact pseudomanifold and a given perversity in the sense of Goresky and MacPherson a Morse theoretical cochain complex, which computes the intersection cohomology of the space. In the second part we use this cochain complex as well as the model Witten Laplacian to define the Bismut-Zhang torsion of a pseudomanifold. Conjecturally the Bismut-Zhang torsion will serve as the "topological" side in a Cheeger-Müller theorem for spaces with iterated conical singularities.Résumé. -Dans la première partie de cet article on construit, en utilisant la théorie de Morse, pour une pseudovariété stratifiée et une perversité au sens de la théorie de Goresky et MacPherson un complexe cohomologique. Ce complexe calcule la cohomologie d'intersection de la pseudovariété. Dans la deuxième partie on utilise ce complexe ainsi que le Laplacien de Witten pour définir la torsion de Bismut-Zhang, qui, conjecturellement, va servir dans un théorème de Cheeger-Müller pour des pseudovariétés à singularités coniques.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

An extension of a theorem by Cheeger and Müller to spaces with isolated conical singularities

Abstract: Differential geometryAn extension of a theorem by Cheeger and Müller to spaces with isolated conical singularities Une extension d'un résultat de Cheeger et Müller pour un espace à singularités coniques isolées

Cited by 2 publications

References 49 publications

Analytic Torsion for Fibred Boundary Metrics and Conic Degeneration

Analytic Torsion for Fibred Boundary Metrics and Conic Degeneration

A Morse-Bott type complex and the Bismut–Zhang torsion for intersection cohomology

Contact Info

Product

Resources

About