Pseudo-Anosov stretch factors and homology of mapping tori

Ian Agol, Christopher J. Leininger, Dan Margalit

Research output: Contribution to journalArticlepeer-review


We consider the pseudo-Anosov elements of the mapping class group of a surface of genus g that fix a rank k subgroup of the first homology of the surface. We show that the smallest entropy among these is comparable to (k+1)/g. This interpolates between results of Penner and of Farb and the second and third authors, who treated the cases of k=0 and k=2g, respectively, and answers a question of Ellenberg. We also show that the number of conjugacy classes of pseudo-Anosov mapping classes as above grows (as a function of g) like a polynomial of degree k.

Original languageEnglish (US)
Pages (from-to)664-682
Number of pages19
JournalJournal of the London Mathematical Society
Issue number3
StatePublished - Jun 13 2016

ASJC Scopus subject areas

  • Mathematics(all)

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