References

Discussions on StackExchange Mathematics

• prove RP3≅SO(3)

• Visualizing the fundamental group of SO(3)

• Bijection between SO(3) and S2×S1

• Why is SO(3) not S1×S2? (Where is the mistake?)

• Homeomorphism of SO(3)?

• SO(3) homeomorphic to RP3

• SO(n) 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/