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Incase anyone doesn't understand the notation, GL(2;C) is the group of linear transformations on C^2 which are invertible. Another way of looking at it is all complex 2x2 matrices with non-zero determinant.

It is fairly easy to show that GL(2;C) is not simply connected (just define a homomorphism that maps an element to its determinant). So here's my question. If it is not simply connected, than what is its universal covering group? All the textbooks I've looked at give many examples of universal covering groups but they never give you any sort of strategy of how to find one, so I have no idea where to start. Anyone know the answer, or have any hints so I can try to figure it out? Thanks

It is fairly easy to show that GL(2;C) is not simply connected (just define a homomorphism that maps an element to its determinant). So here's my question. If it is not simply connected, than what is its universal covering group? All the textbooks I've looked at give many examples of universal covering groups but they never give you any sort of strategy of how to find one, so I have no idea where to start. Anyone know the answer, or have any hints so I can try to figure it out? Thanks

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