2012/10/10 by Yuichi Yamada, Yamada, Yuichi
Mathematics · #14H50 #57M25 #57M27 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:14H50 #msc:57M25 #msc:57M27
paper · pdf · doi:10.48550/arxiv.1210.2905
20 pages, 20 figures
arxiv created 2012/10/10 · arxiv updated 2012/10/11
Divide knots and links, defined by A'Campo in the singularity theory of complex curves, is a method to present knots or links by real plane curves. The present paper is a continuation of the author's previous result that every knot in the major subfamilies of Berge's lens space surgery (i.e., knots yielding a lens space by Dehn surgery) is presented by an L-shaped curve as a divide knot. In the present paper, L-shaped curves are generalized and it is shown that every knot in the minor subfamilies, called sporadic examples, of Berge's lens space surgery is presented by a generalized L-shaped curve as a divide knot. A formula on the surgery coefficients and the presentation is also generalized.