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Mathematisch-Naturwissenschaftliche Fakultät - Jahrgang 2011


Titel The Curve Graph and Surface Construction in S x R
Autor Ingrid Irmer
Publikationsform Dissertation
Abstract Suppose S is an oriented, compact surface with genus at least two. This thesis investigates the \homology curve complex" of S; a modi cation of the curve complex rst studied by Harvey in which the verticies are required to be homologous multicurves. The relationship between arcs in the homology curve graph and surfaces with boundary in S x R is used to devise an algorithm for constructing efficient arcs in the homology multicurve graph. Alternatively, these arcs can be used to study oriented surfaces with boundary in S x R. The intersection number of curves in S x R is de ned by projecting curves into S. It is proven that the best possible bound on the distance between two curves c0 and c1 in the homology curve complex depends linearly on their intersection number, in contrast to the logarithmic bound obtained in the curve complex. The difference in these two results is shown to be partly due to the existence of what Masur and Minsky refer to as large subsurface projections of c0 and c1 to annuli, and partly due to the small amount of ambiguity in de ning this concept. A bound proportional to the square root of the intersection number is proven in the absence of a certain type of large subsurface projection of c0 and c1 to annuli.
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© Universitäts- und Landesbibliothek Bonn | Veröffentlicht: 13.01.2011