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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/​

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