I want to prove that the fundamental group of $GL(n, \mathbb{C}) $ is infinite.
I don't know how to proceed, any hint ?
2026-03-27 02:39:18.1774579158
Fundamental group of $GL(n, \mathbb{C}) $
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The determinant maps it to $\mathbb C^*$, which has the homotopy type of a circle. So you just have to find a continuous map $\mathbb C^*\to GL(n,\mathbb C)$ such that the composition with the determinant is the identity, and apply the $\pi_1$ functor.