Pseudo-cycles of surface-knots

Yashiro, Tsukasa

doi:10.1142/s0218216516500681

J. Knot Theory Ramifications

2016

DOI: 10.1142/s0218216516500681

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Pseudo-cycles of surface-knots

Tsukasa Yashiro

Abstract: In this paper, we describe a two-dimensional rectangular-cell-complex derived from a surface-knot diagram of a surface-knot. We define a pseudo-cycle for a quandle colored surface-knot diagram. We show that the maximal number of pseudo-cycles is a surface-knot invariant.

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2018

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Covering diagrams over surface-knot diagrams

Yashiro

2018

J. Knot Theory Ramifications

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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.

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Covering diagrams over surface-knot diagrams

Yashiro

2018

J. Knot Theory Ramifications

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Pseudo-cycles of surface-knots

Abstract: In this paper, we describe a two-dimensional rectangular-cell-complex derived from a surface-knot diagram of a surface-knot. We define a pseudo-cycle for a quandle colored surface-knot diagram. We show that the maximal number of pseudo-cycles is a surface-knot invariant.

Cited by 1 publication

References 10 publications

Covering diagrams over surface-knot diagrams

Covering diagrams over surface-knot diagrams

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