2006/08/21 by Kazuhiro Ichihara, Ichihara, Kazuhiro, Shigeru Mizushima +1
Computer Science · Mathematics · #57M25 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.GT #msc:57M25 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.math/0608480
13 pages, 10 figures, v2: An assumption of the main theorem is clarified
openalex publication_date 2006/08/21 · arxiv created 2007/02/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The crosscap number of a knot in the 3-sphere is defined as the minimal first Betti number of non-orientable subsurfaces bounded by the knot. In this paper, we determine the crosscap numbers of pretzel knots. The key ingredient to obtain the result is the algorithm of enumerating all essential surfaces for Montesinos knots developed by Hatcher and Oertel.