[PDF] Minimal generating and normally generating sets for the braid and mapping class groups of $$\mathbb{D }^{2}$$, $$\mathbb S ^{2}$$ and $$\mathbb{R P^2}$$ | Semantic Scholar

Minimal generating and normally generating sets for the braid and mapping class groups of $$\mathbb{D }^{2}$$, $$\mathbb S ^{2}$$ and $$\mathbb{R P^2}$$

@article{Gonalves2012MinimalGA,
title={Minimal generating and normally generating sets for the braid and mapping class groups of \$\$\mathbb\{D \}^\{2\}\$\$, \$\$\mathbb S ^\{2\}\$\$ and \$\$\mathbb\{R P^2\}\$\$},
author={D. Gonçalves and John Guaschi},
journal={Mathematische Zeitschrift},
year={2012},
volume={274},
pages={667-683}
}

We consider the (pure) braid groups $$B_{n}(M)$$ and $$P_{n}(M)$$, where $$M$$ is the $$2$$-sphere $$\mathbb S ^{2}$$ or the real projective plane $$\mathbb R P^2$$. We determine the minimal cardinality of (normal) generating sets $$X$$ of these groups, first when there is no restriction on $$X$$, and secondly when $$X$$ consists of elements of finite order. This improves on results of Berrick and Matthey in the case of $$\mathbb S ^{2}$$, and extends them in the case of $$\mathbb R P^2$$. We… CONTINUE READING