Definition
The three-dimensional lens spaces are quotients of by -actions. More precisely, let and be coprime integers and consider as the unit sphere in . Then the -action on generated by
is free as p and q were coprime. The resulting quotient space is called the lens space .
This can be generalized to higher dimensions as follows: Let be integers such that the are coprime to and consider as the unit sphere in . The lens space is the quotient of by the free -action generated by
In three dimensions we have
The fundamental group of all the lens spaces is independent of the .
Read more about this topic: Lens Space
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