منابع مشابه
Simple Curves on Surfaces
We study simple closed geodesics on a hyperbolic surface of genus g with b geodesic boundary components and c cusps. We show that the number of such geodesics of length at most L is of order L. This answers a long-standing open question. Let S be a hyperbolic surface of genus g with c cusps and b boundary components. In this paper we study the set of simple (that is, without selfintersections) ...
متن کاملVeech surfaces and simple closed curves
We study the SL(2,R)–infimal lengths of simple closed curves on half-translation surfaces. Our main result is a characterization of Veech surfaces in terms of these lengths. We also revisit the “no small virtual triangles” theorem of Smillie and Weiss and establish the following dichotomy: the virtual triangle area spectrum of a half-translation surface either has a gap above zero or is dense i...
متن کاملPseudo-anosov Maps and Simple Closed Curves on Surfaces
Suppose C and C are two sets of simple closed curves on a hyperbolic surface F . We will give necessary and sufficient conditions for the existence of a pseudo-Anosov map g such that g(C) ∼= C. Pseudo-Anosov maps are the most important class among surface homeomorphisms [Th3], and they play important roles in 3-manifold theory [Th2]. This note is to address the following question: Suppose F is ...
متن کاملTransforming Curves on Surfaces
We describe an optimal algorithm to decide if one closed curve on a triangulated 2-manifold can be continuously transformed to another, i.e., if they are homotopic. Suppose C 1 and C 2 are two closed curves on a surface M of genus g. Further, suppose T is a triangulation of M of size n such that C 1 and C 2 are represented as edge-vertex sequences of lengths k 1 and k 2 in T , respectively. The...
متن کاملCurves on Normal Surfaces
We study locally Cohen-Macaulay space curves lying on normal surfaces. We prove some theorems on the behaviour of the cohomology functions and initial ideals of such space curves, which give a basic distinction between those curves and curves lying on non-normal surfaces. A natural step in the study and classification of space curves is to classify the Hilbert functions of space curves, or, mor...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 1984
ISSN: 0024-6107
DOI: 10.1112/jlms/s2-29.2.331