Corpus ID: 115167066

# A classification of pairs of disjoint nonparallel primitives in the boundary of a genus two handlebody

@article{Berge2009ACO,
title={A classification of pairs of disjoint nonparallel primitives in the boundary of a genus two handlebody},
author={John Berge},
journal={arXiv: Geometric Topology},
year={2009}
}
• John Berge
• Published 2009
• Mathematics
• arXiv: Geometric Topology
• Embeddings of pairs of disjoint nonparallel primitive simple closed curves in the boundary of a genus two handlebody are classified. Briefly, two disjoint primitives either lie on opposite ends of a product $F \boldsymbol{\times} I$, or they lie on opposite ends of a kind of "twisted" product $F \widetilde{\boldsymbol{\times}} I$, where $F$ is a once-punctured torus. If one of the curves is a proper power of a primitive, the situation is simpler. Either the curves lie on opposite sides of a… CONTINUE READING

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