Two mod-p Johnson filtrations

Date
2014-04-17
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Abstract

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.

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Degree
Doctor of Philosophy
Type
Thesis
Keywords
Geometric topology, Group theory, Mapping class groups
Citation

Cooper, James Michael. "Two mod-p Johnson filtrations." (2014) Diss., Rice University. https://hdl.handle.net/1911/76394.

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