Two mod-p Johnson filtrations

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dc.contributor.advisorPutman, Thomas Andrewen_US
dc.contributor.committeeMemberWolf, Michaelen_US
dc.contributor.committeeMemberHicks, Illya V.en_US
dc.creatorCooper, James Michaelen_US
dc.date.accessioned2014-08-05T16:50:51Zen_US
dc.date.available2014-08-05T16:50:51Zen_US
dc.date.created2014-05en_US
dc.date.issued2014-04-17en_US
dc.date.submittedMay 2014en_US
dc.date.updated2014-08-05T16:50:52Zen_US
dc.description.abstractWe consider two mod-p central series of the free group given by Stallings and Zassenhaus. Applying these series to definitions of Dennis Johnson's filtration of the mapping class group we obtain two mod-p Johnson filtrations. Further, we adapt the definition of the Johnson homomorphisms to obtain mod-p Johnson homomorphisms. We calculate the image of the first of these homomorphisms. We give generators for the kernels of these homomorphisms as well. We restrict the range of our mod-p Johnson homomorphisms using work of Morita. We finally prove the announced result of Perron that a rational homology 3-sphere may be given as a Heegaard splitting with gluing map coming from certain members of our mod-p Johnson filtrations.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationCooper, James Michael. "Two mod-p Johnson filtrations." (2014) Diss., Rice University. <a href="https://hdl.handle.net/1911/76394">https://hdl.handle.net/1911/76394</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/76394en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectGeometric topologyen_US
dc.subjectGroup theoryen_US
dc.subjectMapping class groupsen_US
dc.titleTwo mod-p Johnson filtrationsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematicsen_US
thesis.degree.disciplineNatural Sciencesen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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