Let $$S_g = \langle a_1,b_1,...,a_g,b_g \mid \prod_{i=1}^g[a_i,b_i] = 1 \rangle$$ be the fundamental group of a genus $g$ orientable surface. Is there a nice description of the automorphism group of $S_g$? In particular I would love a nice finite swet of generators.
2026-03-26 21:35:14.1774560914
Automorphism group of a surface group
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