1. Covering diagrams over surface-knot diagrams.
- Author
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Yashiro, Tsukasa
- Subjects
- *
KNOT theory , *GEOMETRIC surfaces , *CHARTS, diagrams, etc. , *GEOMETRIC topology , *MATHEMATICS - Abstract
A surface-knot is a closed oriented surface smoothly embedded in 4-space and a surface-knot diagram is a projected image of a surface-knot under the orthogonal projection in 3-space with crossing information. Every surface-knot diagram induces a rectangular-cell complex. In this paper, we introduce a covering diagram over a surface-knot diagram. the covering map induces a covering of the rectangular-cell complexes. As an application, a lower bound of triple point numbers for a family of surface-knots is obtained. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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