I need to prove that $O(3,19)/SO(2)\times O(1,19)$ is simply connected. In particular $O(n_{+},n_{-})$ denotes the orthogonal group of $\mathbb{R}^{n_{+}+n_{-}}$ endowed with the diagonal quadratic form $diag(1,\cdots,1,-1,\cdots,-1)$ of signature $(n_{+},n_{-})$. I don't know much about the subject, and i don't know how to prove the statement
How to prove that a lie group is simply connected
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algebraic-topology
lie-groups
homotopy-theory
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2Isn't it more natural to assume he means to mod out by the subgroup $SO(2) \times O(1,19)$? – 2014-02-14