The moduli stacks of semi-stable vector bundles and certain parabolic variants on a curve are A^1-connected.
Morel, The stable A ^1 -connectivity theorems, K-Theory 35 (2005), 1–68
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$\mathbb{A}^1$--connectedness of moduli stack of semi-stable and parabolic semi-stable vector bundles over a curve
The moduli stacks of semi-stable vector bundles and certain parabolic variants on a curve are A^1-connected.