Constructing seifert surfaces from n-bridge link projections

Joan E. Licata

doi:10.1142/S021821651000784X

Constructing seifert surfaces from n-bridge link projections

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

Abstract

This paper presents a new algorithm for constructing Seifert surfaces from n-bridge projections of links. The algorithm, 21, produces minimal complexity surfaces for large classes of braids and alternating links. In addition, we consider a family of knots for which canonical genus is strictly greater than genus, (g_c(K) > g(K)), and show that builds surfaces realizing the knot genus g(K). We also present a generalization of Seifert's algorithm which constructs surfaces representing arbitrary relative second homology classes in a link complement.

Original language	English
Pages (from-to)	313-334
Number of pages	22
Journal	Journal of Knot Theory and its Ramifications
Volume	19
Issue number	3
DOIs	https://doi.org/10.1142/S021821651000784X
Publication status	Published - Mar 2010
Externally published	Yes

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abstract = "This paper presents a new algorithm for constructing Seifert surfaces from n-bridge projections of links. The algorithm, 21, produces minimal complexity surfaces for large classes of braids and alternating links. In addition, we consider a family of knots for which canonical genus is strictly greater than genus, (gc(K) > g(K)), and show that builds surfaces realizing the knot genus g(K). We also present a generalization of Seifert's algorithm which constructs surfaces representing arbitrary relative second homology classes in a link complement.",

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AB - This paper presents a new algorithm for constructing Seifert surfaces from n-bridge projections of links. The algorithm, 21, produces minimal complexity surfaces for large classes of braids and alternating links. In addition, we consider a family of knots for which canonical genus is strictly greater than genus, (gc(K) > g(K)), and show that builds surfaces realizing the knot genus g(K). We also present a generalization of Seifert's algorithm which constructs surfaces representing arbitrary relative second homology classes in a link complement.

KW - Knot theory

KW - Minimal complexity surfaces

KW - Seifert surface

KW - Thurston norm

UR - https://www.scopus.com/pages/publications/77951683429

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DO - 10.1142/S021821651000784X

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JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

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Constructing seifert surfaces from n-bridge link projections

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