dc.contributor.author Cekic, Mihajlo dc.contributor.author Delarue, Benjamin dc.contributor.author Dyatlov, Semyon dc.contributor.author Paternain, Gabriel dc.date.accessioned 2022-06-10T16:00:39Z dc.date.available 2022-06-10T16:00:39Z dc.date.issued 2022-07 dc.date.submitted 2021-02-27 dc.identifier.issn 0020-9910 dc.identifier.other s00222-022-01108-x dc.identifier.other 1108 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/337993 dc.description Funder: Massachusetts Institute of Technology (MIT) dc.description.abstract We show that for a generic conformal metric perturbation of a compact hyperbolic 3-manifold $\Sigma$ with Betti number $b_1$, the order of vanishing of the Ruelle zeta function at zero equals $4-b_1$, while in the hyperbolic case it is equal to $4-2b_1$. This is in contrast to the 2-dimensional case where the order of vanishing is a topological invariant. The proof uses the microlocal approach to dynamical zeta functions, giving a geometric description of generalized Pollicott-Ruelle resonant differential forms at 0 in the hyperbolic case and using first variation for the perturbation. To show that the first variation is generically nonzero we introduce a new identity relating pushforwards of products of resonant and coresonant 2-forms on the sphere bundle $S\Sigma$ with harmonic 1-forms on $\Sigma$. dc.language en dc.publisher Springer Science and Business Media LLC dc.subject Article dc.title The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds dc.type Article dc.date.updated 2022-06-10T16:00:38Z prism.endingPage 394 prism.issueIdentifier 1 prism.publicationName INVENTIONES MATHEMATICAE prism.startingPage 303 prism.volume 229 dc.identifier.doi 10.17863/CAM.85398 dcterms.dateAccepted 2022-02-08 rioxxterms.versionofrecord 10.1007/s00222-022-01108-x rioxxterms.version VoR rioxxterms.licenseref.uri http://creativecommons.org/licenses/by/4.0/ dc.contributor.orcid Cekić, Mihajlo [0000-0002-7565-4127] dc.contributor.orcid Delarue, Benjamin [0000-0002-2400-022X] dc.contributor.orcid Dyatlov, Semyon [0000-0002-6594-7604] dc.identifier.eissn 1432-1297 dc.publisher.url http://dx.doi.org/10.1007/s00222-022-01108-x cam.issuedOnline 2022-03-11
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