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    • Generating the Johnson filtration 

      Church, Thomas; Putman, Andrew (2015)
      For k≥1, let J1g(k) be the k th term in the Johnson filtration of the mapping class group of a genus g surface with one boundary component. We prove that for all k≥1, there exists some Gk≥0 such that J1g(k) is generated ...
    • Small generating sets for the Torelli group 

      Putman, Andrew (2012)
      Proving a conjecture of Dennis Johnson, we show that the Torelli subgroup Ig of the genus g mapping class group has a finite generating set whose size grows cubically with respect to g. Our main tool is a new space called ...