Consider the group $G = \left\{\begin{pmatrix} a & b\\ 0 & 1\end{pmatrix}: a \in \mathbb{C}^{\times}, b \in \mathbb{C}\right\} \subset GL(2, \mathbb{C})$. How does one find the universal cover of this group? In general, if I had a larger explicit matrix, what would I do?
Finding the universal cover of a matrix group
8
$\begingroup$
algebraic-topology
lie-groups
-
0I changed the tags to two that I thought were most specific -- feel free to revert. Interesting question! – 2012-04-02
-
0Do you know how to find the universal cover of $G$ as a topological space, and how to write down the covering map? From there it suffices to figure out how to lift the group structure. – 2012-04-02
-
0Er, no actually, how would I go about doing that? – 2012-04-02
-
1@109230: okay. Do you know how to find the universal cover of $\mathbb{C}^{\times}$? – 2012-04-03