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Tight upper bounds on the number of invariant components on translation surfaces

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Abstract

An abelian differential on a surface defines a flat metric and a vector field on the complement of a finite set of points. The vertical flow that can be defined on the surface has two kinds of invariant closed sets (i.e. invariant components) — periodic components and minimal components. We give upper bounds on the number of minimal components, on the number of periodic components and on the total number of invariant components in every stratum of abelian differentials. We also show that these bounds are tight in every stratum.

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Authors and Affiliations

  1. Department of Mathematics, Ben Gurion University, Be’er Sheva, Israel, 84105

    Yoav Naveh

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  1. Yoav Naveh
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Correspondence to Yoav Naveh.

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Naveh, Y. Tight upper bounds on the number of invariant components on translation surfaces. Isr. J. Math. 165, 211–231 (2008). https://doi.org/10.1007/s11856-008-1010-5

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  • DOI: https://doi.org/10.1007/s11856-008-1010-5

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