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Rel leaves of the Arnoux-Yoccoz surfaces
Hooper, W. Patrick...

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Rel leaves of the Arnoux-Yoccoz surfaces by Hooper, W. Patrick ( Author )
Lemonjar Open Access
N.A
01-01-2015
We analyze the rel leaves of the Arnoux-Yoccoz translation surfaces. We show that for any genus g≥3, the leaf is dense in the connected component of the stratum H(g−1,g−1) to which it belongs, and the one-sided imaginary-rel trajectory of the surface is divergent. For one surface on this trajectory, namely the Arnoux-Yoccoz surface itself, the horizontal foliation is invariant under a pseudo-Anosov map (and in particular is uniquely ergodic), but for all other surfaces, the horizontal foliation is completely periodic. The appendix proves a field theoretic result needed for denseness of the leaf: for any n≥3, the field extension of the rationals obtained by adjoining a root of Xn−Xn−1−…−X−1 has no totally real subfields other than the rationals.
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English
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MYR 0.00
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doi:10.1007/s00029-017-0367-x
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