Geometric Topology (The Geometry Junkyard)
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|David Eppstein, Theory Group, ICS, UC Irvine|
|An extensive annotated list of links to material in an area of mathematics that concerns the assignment of geometric structures to topological spaces, so that they "look like" geometric spaces. For instance, compact two-dimensional surfaces can have a local geometry based on the sphere (the sphere itself, and the projective plane), based on the Euclidean plane (the torus and the Klein bottle), or based on the hyperbolic plane (all other surfaces). Similar questions in three dimensions have more complicated answers; Thurston showed that there are eight possible geometries, and conjectured that all 3-manifolds can be split into pieces having these geometries. Computer solution of these questions by programs like SnapPea has proved very useful in the study of knot theory and other topological problems.|
|Levels:||High School (9-12), College, Research|
|Resource Types:||Link Listings, Topic Tools Miscellaneous|
|Math Topics:||Symmetry/Tessellations, Topology|
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