Advanced Search
Article Contents
Article Contents

Algebraically periodic translation surfaces

Abstract Related Papers Cited by
  • We develop an algebraic framework for studying translation surfaces. We study the Sah--Arnoux--Fathi-invariant and the collection of directions in which it vanishes. We show that these directions are described by a number field which we call the periodic direction field. We study the $J$-invariant of a translation surface, introduced by Kenyon and Smillie and used by Calta. We relate the $J$-invariant to the periodic direction field. For every number field $K\subset\ \mathbb R$ we show that there is a translation surface for which the periodic direction field is $K$. We study automorphism groups associated to a translation surface and relate them to the $J$-invariant. We relate the existence of decompositions of translation surfaces into squares with the total reality of the periodic direction field.
    Mathematics Subject Classification: Primary: 57M50, Secondary: 37D50, 30F30.


    \begin{equation} \\ \end{equation}
  • 加载中

Article Metrics

HTML views() PDF downloads(76) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint