Putman, Thomas Andrew2014-08-052014-08-052014-052014-04-17May 2014Cooper, 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>.https://hdl.handle.net/1911/76394We 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.application/pdfengCopyright 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.Geometric topologyGroup theoryMapping class groupsThesis2014-08-05