Two mod-p Johnson filtrations

James Cooper

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arXiv · 1402.4186

Two mod-p Johnson filtrations

James Cooper

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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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James Cooper. 2014-02-18. Two mod-p Johnson filtrations. https://arxiv.org/abs/1402.4186

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