Cannon-Thurston fibers for iwip automorphisms of FN

Ilya Kapovich, Martin Lustig

Research output: Contribution to journalArticlepeer-review

Abstract

For any atoroidal iwip ℓ Out(FN), the mapping torus group G =FN t is hyperbolic, and, by a result of Mitra, the embedding iota: FN hd G induces a continuous, FN-equivariant and surjective Cannon-Thurston map FN to G. We prove that for any as above, the map is finite-to-one and that the preimage of every point of G has cardinality at most 2N. We also prove that every point S in G with at least three preimages in FN has the form (wtm) where w FN, m ne 0, and that there are at most 4N-5 distinct FN-orbits of such singular points in G (for the translation action of FN on G). By contrast, we show that for k=1,2, there are uncountably many points S G (and thus uncountably many FN-orbits of such S) with exactly k preimages in FN.

Original languageEnglish (US)
Pages (from-to)203-224
Number of pages22
JournalJournal of the London Mathematical Society
Volume91
Issue number1
DOIs
StatePublished - Apr 17 2015

ASJC Scopus subject areas

  • General Mathematics

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