Crosscap numbers of pretzel knots |
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| Authors: | Kazuhiro Ichihara Shigeru Mizushima |
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| Affiliation: | aCollege of General Education, Osaka Sangyo University, 3-1-1 Nakagaito, Daito, Osaka 574-8530, Japan;bDepartment of Mathematical and Computing Sciences, Tokyo Institute of Technology, 2-12-1 Ohokayama, Meguro, Tokyo 152-8552, Japan |
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| Abstract: | ![]()
The crosscap number of a knot in the 3-sphere is defined as the minimal first Betti number of non-orientable surfaces bounded by the knot. In this paper, we determine the crosscap numbers of a large class 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. |
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| Keywords: | Crosscap number Pretzel knot |
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