Mathematics – Group Theory
Scientific paper
2010-06-11
Mathematics
Group Theory
Scientific paper
Let $S_{g,1,p}$ be an orientable surface of genus $g$ with one boundary component and $p$ punctures. Let $\mathcal{M}_{g,1,p}$ be the mapping-class group of $S_{g,1,p}$ relative to the boundary. We construct homomorphisms $\mathcal{M}_{g,1,p} \to \mathcal{M}_{g',1,(b-1)}$, where $g' \geq 0$ and $b\geq 1$. 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.
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