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dc.contributor.authorChurch, Thomas
Putman, Andrew
dc.date.accessioned 2017-05-12T15:04:32Z
dc.date.available 2017-05-12T15:04:32Z
dc.date.issued 2015
dc.identifier.citation Church, Thomas and Putman, Andrew. "Generating the Johnson filtration." Geometry & Topology, 19, (2015) Mathematical Sciences Publishers: 2217-2255. http://dx.doi.org/10.2140/gt.2015.19.2217.
dc.identifier.urihttps://hdl.handle.net/1911/94227
dc.description.abstract For k≥1, let J1g(k) be the k th term in the Johnson filtration of the mapping class group of a genus g surface with one boundary component. We prove that for all k≥1, there exists some Gk≥0 such that J1g(k) is generated by elements which are supported on subsurfaces whose genus is at most Gk. We also prove similar theorems for the Johnson filtration of Aut(Fn) and for certain mod-p analogues of the Johnson filtrations of both the mapping class group and of Aut(Fn). The main tools used in the proofs are the related theories of FI–modules (due to the first author with Ellenberg and Farb) and central stability (due to the second author), both of which concern the representation theory of the symmetric groups over Z.
dc.language.iso eng
dc.publisher Mathematical Sciences Publishers
dc.rights Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
dc.title Generating the Johnson filtration
dc.type Journal article
dc.citation.journalTitle Geometry & Topology
dc.subject.keywordmapping class group
Torelli group
Johnson filtration
automorphism group of free group
FI–modules
dc.citation.volumeNumber 19
dc.type.dcmi Text
dc.identifier.doihttp://dx.doi.org/10.2140/gt.2015.19.2217
dc.type.publication publisher version
dc.citation.firstpage 2217
dc.citation.lastpage 2255


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