Skip to main content Accessibility help
×
Home
Hostname: page-component-59df476f6b-pc27v Total loading time: 0.135 Render date: 2021-05-18T22:41:17.394Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true }

Lefschetz formulae for Anosov flows on 3-manifolds

Published online by Cambridge University Press:  19 September 2008

Héctor Sánchez-Morgado
Affiliation:
Institute de Matematicas, Universidad Nacional Autónoma de México, Ciudad Universitaria CP 04510, Mexico D.F., Mexico

Abstract

Fried has related closed orbits of the geodesic flow of a surface S of constant negative curvature to the R-torsion for a unitary representation of the fundamental group of the unit tangent bundle T1S. In this paper we extend those results to transitive Anosov flows and 2-dimensional attractors on 3-manifolds.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1993

Access options

Get access to the full version of this content by using one of the access options below.

References

[1]Bott, R. & Tu, L. W.. Differential Forms in Algebraic Topology, GTM 82. Springer, New York, 1981.Google Scholar
[2]Christy, J.. Branched surfaces and attractors I: dynamic branched surfaces.Google Scholar
[3]Fried, D.. Fuchsian groups and Reidemeister torsion. Contemp. Math. S3 (1986), 141163.CrossRefGoogle Scholar
[4]Fried, D.. The zeta functions of Ruelle and Selberg I. Ann. Sci. ENS 19 (1986), 491517.Google Scholar
[5]Fried, D.. Lefschetz formulae for flows. Contemp. Math. 58 (1987), 1969.CrossRefGoogle Scholar
[6]Ratner, M.. Markov decomposition for a Y-flow on a three-dimensional manifold. Math. Notes 6 (1969), 880886.CrossRefGoogle Scholar
[7]Ruelle, D.. Zeta functions for expanding maps and Anosov flows. Invent. Math. 34 (1976), 231242.CrossRefGoogle Scholar

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Lefschetz formulae for Anosov flows on 3-manifolds
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Lefschetz formulae for Anosov flows on 3-manifolds
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Lefschetz formulae for Anosov flows on 3-manifolds
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *