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Surfaces associated to a knotted space curve
by
Barbara Jablonska
TU Berlin
From any smooth knot K in 3-space, we derive three surfaces with maps to S^2. These represent certain geometric features of the knot diagrams obtained as the orthogonal projections of K in all possible directions. It turns out that these surfaces have the same boundary curves and fold lines on S^2. One can cut them apart and reglue in various different manners obtaining in each case a different compact 2-manifold with a map to S^2. The degrees of these maps yield some interesting results. E.g. in one case the degree is the self-linking number of the initial curve, and the orientation of the manifold prescribes how to compute it from a diagram.
Date received: November 11, 2008
Copyright © 2008 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # caxq-18.