The Nielsen-Thurston Classification Theorem
نویسنده
چکیده
Overview: The Nielsen-Thurston Classification Theorem asserts that every element of MCG(Sg) (g ≥ 2) exhibits one of three types of simple behavior. It either has finite order, fixes a nonempty set of of isotopy classes of essential, simple closed curves (reducible), or stretches along a pair of transverse measured foliations in an area-preserving way (pseduo-Anosov). Bers’ strategy for proving these results relies on the general yoga of geometric group theory: understanding a group by the way that it acts on a particular space. The space in question turns out to be the Teichmuller space Teich(Sg) of the surface, endowed with the so-called Teichmuller metric.
منابع مشابه
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