Kapovich, Michael Department of Mathematics, University of California, Davis, California.
Last reviewed:June 2015
- Constructing spaces from building blocks
- Hyperbolic geometry
- Thurston's geometrization conjecture
- Ricci flow
- Perelman's work
- Mathematical significance
- Relevance outside of mathematics
- Related Primary Literature
- Additional Reading
Thurston's geometrization conjecture (now, a theorem of Grigory Perelman), which aims to answer the question: How could one describe the possible shapes of our universe? Here we will be assuming (although, some scientists think otherwise) that our space is 3-dimensional (3-D) [it has three directions: width, depth, and height]; closed (which means that you cannot travel infinitely far away from a given point in space, and that it does not have a boundary); connected (you can get from any point to any point); and orientable (if you travel along a path and return to the point of departure, your left and right hands will not get switched).
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