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
Famous quotes containing the word definition:
“Mothers often are too easily intimidated by their children’s negative reactions...When the child cries or is unhappy, the mother reads this as meaning that she is a failure. This is why it is so important for a mother to know...that the process of growing up involves by definition things that her child is not going to like. Her job is not to create a bed of roses, but to help him learn how to pick his way through the thorns.”
—Elaine Heffner (20th century)
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)
“It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.””
—Jane Adams (20th century)