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Putman, Thomas Andrew Wolf, Michael Hicks, Illya V. Cooper, James Michael 2014-08-05T16:50:51Z 2014-08-05T16:50:51Z 2014-05 2014-04-17 May 2014 2014-08-05T16:50:52Z Cooper, 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/1911/76394 We 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/pdf eng Copyright 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 topology Group theory Mapping class groups Two mod-p Johnson filtrations Thesis Text Mathematics Natural Sciences Rice University Doctoral Doctor of Philosophy open.access