> For the complete documentation index, see [llms.txt](https://wiki.hanzheteng.com/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://wiki.hanzheteng.com/math/topology/references.md).

# References

### Discussions on StackExchange Mathematics

* [prove RP3≅SO(3)](<https://math.stackexchange.com/questions/1688179/prove-rp3-cong-so3 >)
* [Visualizing the fundamental group of SO(3)](https://math.stackexchange.com/questions/17856/visualizing-the-fundamental-group-of-so3)
* [Bijection between SO(3) and S2×S1](https://math.stackexchange.com/questions/1934931/bijection-between-so3-and-s2-times-s1)
* [Why is SO(3) not S1×S2? (Where is the mistake?)](https://math.stackexchange.com/questions/1120283/why-is-so3-not-s1-times-s2-where-is-the-mistake)
* [Homeomorphism of SO(3)?](https://math.stackexchange.com/questions/1737265/homeomorphism-of-so3)
* [SO(3) homeomorphic to RP3](https://math.stackexchange.com/questions/1814761/so3-homeomorphic-to-mathbbrp3)
* [SO(n) homeomorphic to cartesian product of spheres](https://math.stackexchange.com/questions/1515687/son-homeomorphic-to-cartesian-product-of-spheres)

### Articles by Qiaochu Yuan

* <https://qchu.wordpress.com/2011/02/05/so3-and-su2/>
* <https://qchu.wordpress.com/2011/02/12/su2-and-the-quaternions/>
  * S^1≅SO(2) and e^ix=cos⁡x+i sin⁡x, group of elements of norm 1 in complex numbers
  * S^3≅SO(3) and SU(2) is isomorphic to the group of elements of norm 1 in quaternions

### Other References

* <http://motion.pratt.duke.edu/RoboticSystems/3DRotations.html>
* "The Very Basics of Groups, Rings, and Fields" by Ben Brubaker. (Z/nZ is a fancy notation for the integers mod n under addition.)
* "The Quaternions and the Spaces S3, SU(2), SO(3), and RP3" by Jean Gallier.
* "An Elementary Introduction to Groups and Representations" by Brian C. Hall.

### One More Thing

* You can always ask ChatGPT: <https://chat.openai.com/>