Homomorphisms between pure mapping class groups

Rodrigo de Pool

Homomorphisms between pure mapping class groups

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arxiv 2410.18796 v2 pith:JY4W7JKI submitted 2024-10-24 math.GT math.GR

Rodrigo de Pool This is my paper · ORCID

classification math.GTmath.GR

keywords pmaptextclassgroupshomomorphismsmappingpureapplication

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abstract

Let $S$ and $S'$ be orientable finite-type surfaces of genus $g\geq 4$ and $g'$, respectively. We prove that every multitwist-preserving map between pure mapping class groups $\text{PMap}(S)\to \text{PMap}(S')$ is induced by a multi-embedding. As an application, we classify all homomorphisms $\text{PMap}(S)\to \text{PMap}(S')$ for $g\geq 4$ and $g' \leq 6\cdot 2^{g-4}$.

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Holomorphic maps between moduli spaces II
math.GT 2024-12 conditional novelty 6.0 of 10

For g>=4 and g'<=3*2^(g-3), every non-constant holomorphic map between moduli spaces is a forgetful map.

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