A rubber band is stretched around a pebble, and it crosses itself at several points (see Figure 1). The combinatorics of self-crossings can be described by a closed plane curve—it is the rubber band in a parameterization of the surface with one point removed. For example, if you could turn the pebble around, you would see that the self-crossings are described by the plane curve in Figure 1(b). We assume that the surface of the pebble is strongly convex, smooth, and frictionless; in this case, the rubber band models a closed geodesic. Suppose that we are interested in possible patterns of self-crossings. More precisely, what are the possible combinatoric types of self-crossings of a closed geodesic on a strongly convex smooth closed surface?
|Work Title||Self-crossing geodesics|
|License||In Copyright (Rights Reserved)|
|Publication Date||October 28, 2021|
|Publisher Identifier (DOI)||
|Deposited||August 24, 2022|
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