Irreducible non-cyclic braid homomorphisms B_n o B_m (n≥5,m≥3) force m=n and central equivalence to an automorphism, implying holomorphic configuration-space maps are affine to the identity or constant.
Holomorphic maps between moduli spaces II
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We prove that forgetful maps are the only non-constant holomorphic maps $\mathcal{M}_{g,r}\to \mathcal{M}_{g',r'}$ between moduli spaces, as long as $g\ge 4$ and $g'\le 3\cdot 2^{g-3}$.
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Rigidity of maps between configuration spaces
Irreducible non-cyclic braid homomorphisms B_n o B_m (n≥5,m≥3) force m=n and central equivalence to an automorphism, implying holomorphic configuration-space maps are affine to the identity or constant.