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dc.contributor.authorCekic, Mihajlo
dc.contributor.authorDelarue, Benjamin
dc.contributor.authorDyatlov, Semyon
dc.contributor.authorPaternain, Gabriel
dc.date.accessioned2022-06-10T16:00:39Z
dc.date.available2022-06-10T16:00:39Z
dc.date.issued2022-07
dc.date.submitted2021-02-27
dc.identifier.issn0020-9910
dc.identifier.others00222-022-01108-x
dc.identifier.other1108
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/337993
dc.descriptionFunder: Massachusetts Institute of Technology (MIT)
dc.description.abstractWe 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.languageen
dc.publisherSpringer Science and Business Media LLC
dc.subjectArticle
dc.titleThe Ruelle zeta function at zero for nearly hyperbolic 3-manifolds
dc.typeArticle
dc.date.updated2022-06-10T16:00:38Z
prism.endingPage394
prism.issueIdentifier1
prism.publicationNameINVENTIONES MATHEMATICAE
prism.startingPage303
prism.volume229
dc.identifier.doi10.17863/CAM.85398
dcterms.dateAccepted2022-02-08
rioxxterms.versionofrecord10.1007/s00222-022-01108-x
rioxxterms.versionVoR
rioxxterms.licenseref.urihttp://creativecommons.org/licenses/by/4.0/
dc.contributor.orcidCekić, Mihajlo [0000-0002-7565-4127]
dc.contributor.orcidDelarue, Benjamin [0000-0002-2400-022X]
dc.contributor.orcidDyatlov, Semyon [0000-0002-6594-7604]
dc.identifier.eissn1432-1297
dc.publisher.urlhttp://dx.doi.org/10.1007/s00222-022-01108-x
cam.issuedOnline2022-03-11


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