Out(F3) Index Realization

Author:

PFAFF CATHERINE

Abstract

AbstractBy proving precisely which singularity index lists arise from the pair of invariant foliations for a pseudo-Anosov surface homeomorphism, Masur and Smillie [MS93] determined a Teichmüller flow invariant stratification of the space of quadratic differentials. In this paper we determine an analog to the theorem forOut(F3). That is, we determine which index lists permitted by the [GJLL98] index sum inequality are achieved by ageometric fully irreducible outer automorphisms of the rank-3 free group.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference31 articles.

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2. Quadratic differentials with prescribed singularities and pseudo-Anosov diffeomorphisms

3. IRREDUCIBLE AUTOMORPHISMS OF $F_{n}$ HAVE NORTH–SOUTH DYNAMICS ON COMPACTIFIED OUTER SPACE

4. Hyperelliptic components of the moduli spaces of quadratic differentials with prescribed singularities

5. C. Pfaff Ideal Whitehead graphs in Out(Fr ) I: some unachieved graphs. To appear in New York J. Math. arXiv preprint arXiv:1210.5762 (2012).

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3. Cannon–Thurston maps for hyperbolic free group extensions;Israel Journal of Mathematics;2016-10

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