Covering diagrams over surface-knot diagrams

Tsukasa Yashiro

doi:10.1142/S0218216518500426

Covering diagrams over surface-knot diagrams

Tsukasa Yashiro^*

^*Corresponding author for this work

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

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 nformation. 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.

Original language	English
Article number	1850042
Journal	Journal of Knot Theory and its Ramifications
Volume	27
Issue number	6
DOIs	https://doi.org/10.1142/S0218216518500426
Publication status	Published - May 1 2018

Keywords

covering diagram
pseudo-cycle
Surface-knot
triple point

ASJC Scopus subject areas

Algebra and Number Theory

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10.1142/S0218216518500426

Cite this

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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 nformation. 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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AB - 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 nformation. 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.

KW - covering diagram

KW - pseudo-cycle

KW - Surface-knot

KW - triple point

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Covering diagrams over surface-knot diagrams

Abstract

Keywords

ASJC Scopus subject areas

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