Two mod-p Johnson filtrations

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dc.contributor.advisorPutman, Thomas Andrew
dc.contributor.committeeMemberWolf, Michael
dc.contributor.committeeMemberHicks, Illya V.
dc.creatorCooper, James Michael
dc.date.accessioned2014-08-05T16:50:51Z
dc.date.available2014-08-05T16:50:51Z
dc.date.created2014-05
dc.date.issued2014-04-17
dc.date.submittedMay 2014
dc.date.updated2014-08-05T16:50:52Z
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.
dc.format.mimetypeapplication/pdf
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>.
dc.identifier.urihttps://hdl.handle.net/1911/76394
dc.language.isoeng
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.
dc.subjectGeometric topology
dc.subjectGroup theory
dc.subjectMapping class groups
dc.titleTwo mod-p Johnson filtrations
dc.typeThesis
dc.type.materialText
thesis.degree.departmentMathematics
thesis.degree.disciplineNatural Sciences
thesis.degree.grantorRice University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy
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