Infinite presentations for fundamental groups of surfaces

Abstract

For any finite type connected surface $S$, we give an infinite presentation of the fundamental group ${\pi }_1(S,\ast )$ of $S$ based at an interior point $\ast \in S$ whose generators are represented by simple loops. When $S$ is non-orientable, we also give an infinite presentation of the subgroup of ${\pi }_1(S,\ast )$ generated by elements which are represented by simple loops whose regular neighborhoods are annuli.

arXiv comment21 pages, 7 figures

Cited by in corpus (1)

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