A classification of pairs of disjoint nonparallel primitives in the boundary of a genus two handlebody
Abstract
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 oncepunctured 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 separating disk in the handlebody, or they bound a nonseparating essential annulus in the handlebody.
 Publication:

arXiv eprints
 Pub Date:
 October 2009
 arXiv:
 arXiv:0910.3038
 Bibcode:
 2009arXiv0910.3038B
 Keywords:

 Mathematics  Geometric Topology
 EPrint:
 13 pages, 9 figures