Generalizations and Special Cases

**Matt Chisholm
matt@theory.org**

I examine the general mathematical object that is the sphere. First, I examine several constructions general to all spheres. Then, I look at the Clifford Tori, the Hopf Fibration, group structure and surgery in
, with respect to the unique structure of
. Finally, I examine a unique dissection of
which takes advantage of a certain triangulation and the Clifford Tori. This dissection can be used to explain surgery on the unknot in an interesting way.

- Overview of the Sphere
- Visualizing the N-Sphere
- Inversion
- Clifford Tori and Hopf Fibration
- Triangulation of
- Surgery on Knots
- A visualization of The Clifford Tori, Triangulation, and Surgery
- Conclusion
- References
- About this document ...

Adric 2001-03-23