Home / Publications / Preprints / Embedding mapping-class groups of orientable surfaces with one boundary component

Lluis Bacardit (2010)

Embedding mapping-class groups of orientable surfaces with one boundary component

arXiv:1006.2297.

Let \$S\_\ɡ,1,p\\$ be an orientable surface of genus \$g\$ with one boundary component and \$p\$ punctures. Let \$mathcal\M\\_\ɡ,1,p\\$ be the mapping-class group of \$S\_\ɡ,1,p\\$ relative to the boundary. We construct homomorphisms \$mathcal\M\\_\ɡ,1,p\ to mathcal\M\\_\g',1,(b-1)\\$, where \$g' geq 0\$ and \$bgeq 1\$. We proof that the constructed homomorphisms \$M\_\g,1,p\ to M\_\g',1,(b-1)\\$ are injective. One of these embeddings for \$g = 0\$ is classic.

Mathematics - Group Theory

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