Endomorphisms, train track maps, and fully irreducible monodromies

  title={Endomorphisms, train track maps, and fully irreducible monodromies},
  author={Spencer Dowdall and Ilya Kapovich and Christopher J. Leininger},
  journal={arXiv: Group Theory},
  • Spencer Dowdall, Ilya Kapovich, Christopher J. Leininger
  • Published 2015
  • Mathematics
  • arXiv: Group Theory
  • Any endomorphism of a finitely generated free group naturally descends to an injective endomorphism of its stable quotient. In this paper, we prove a geometric incarnation of this phenomenon: namely, that every expanding irreducible train track map inducing an endomorphism of the fundamental group gives rise to an expanding irreducible train track representative of the injective endomorphism of the stable quotient. As an application, we prove that the property of having fully irreducible… CONTINUE READING

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