A complete invariant for connected surfaces in the 3-sphere-Reference-Cited by-同舟云学术

A complete invariant for connected surfaces in the 3-sphere

Published:2020-01 Issue:01 Volume:29 Page:1950091
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Bellettini Giovanni¹²,Paolini Maurizio³,Wang Yi-Sheng⁴^ORCID

Affiliation:

1. Dipartimento di Ingegneria dell’Informazione e Scienze Matematiche, Università di Siena, 53100 Siena, Italy

2. International Centre for Theoretical Physics ICTP, Mathematics Section, 34151 Trieste, Italy

3. Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, 25121 Brescia, Italy

4. National Center for Theoretical Sciences, Mathematics Division, 106 Taipei City, Taiwan

Abstract

We construct a complete invariant of oriented connected closed surfaces in [Formula: see text], which generalizes the notion of peripheral system of a knot group. As an application, we define two computable invariants to investigate handlebody knots and bi-knotted surfaces with homeomorphic complements. In particular, we obtain an alternative proof of inequivalence of Ishii, Kishimoto, Moriuchi and Suzuki’s handlebody knots [Formula: see text] and [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216519500913

Reference30 articles.

1. Shape Reconstruction from Apparent Contours

2. Sur les difféomorphismes de la sphère de dimension trois (Γ4 = O)

3. A Primer on Mapping Class Groups

4. On the Imbedding of Polyhedra in 3-Space

5. On the complementary domains of a certain pair of inequivalent knots

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1. A complete invariant for closed surfaces in the three-sphere;Journal of Knot Theory and Its Ramifications;2021-05