Abstract
This paper concerns thin presentations of knots in closed –manifolds which produce by Dehn surgery, for some slope . If does not have a lens space as a connected summand, we first prove that all such thin presentations, with respect to any spine of have only local maxima. If is a lens space and has an essential thin presentation with respect to a given standard spine (of lens space ) with only local maxima, then we show that is a –bridge or –bridge braid in ; furthermore, we prove the minimal intersection between and such spines to be at least three, and finally, if the core of the surgery yields by –Dehn surgery, then we prove the following inequality: , where is the genus of .
Citation
A Deruelle. D Matignon. "Thin presentation of knots and lens spaces." Algebr. Geom. Topol. 3 (2) 677 - 707, 2003. https://doi.org/10.2140/agt.2003.3.677
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