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A table of n-component handlebody links of genus n+1 up to six crossings

Part of: Graph theory Low-dimensional topology

Published online by Cambridge University Press:  17 June 2022

GIOVANNI BELLETTINI ,
GIOVANNI PAOLINI ,
MAURIZIO PAOLINI  and
YI-SHENG WANG
GIOVANNI BELLETTINI
Affiliation:
Dipartimento di Ingegneria dell’Informazione e Scienze Matematiche, Università di Siena, 53100 Siena, Italy and International Centre for Theoretical Physics ICTP, Mathematics Section, 34151 Trieste, Italy. e-mail: bellettini@diism.unisi.it
GIOVANNI PAOLINI
Affiliation:
California Institute of Technology, Pasadena CA, U.S.A. (work done while at University of Fribourg, Department of Mathematics, 1700 Fribourg, Switzerland). e-mail: paolini@caltech.edu
MAURIZIO PAOLINI
Affiliation:
Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, 25121 Brescia, Italy. e-mail: maurizio.paolini@unicatt.it
YI-SHENG WANG
Affiliation:
Institute of Mathematics, Academia Sinica, Taipei 106, Taiwan. e-mail: yisheng@gate.sinica.edu.tw
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Abstract

A handlebody link is a union of handlebodies of positive genus embedded in 3-space, which generalises the notion of links in classical knot theory. In this paper, we consider handlebody links with a genus two handlebody and $n-1$ solid tori, $n>1$ . Our main result is the classification of such handlebody links with six crossings or less, up to ambient isotopy.

MSC classification

Primary: 57M15: Relations with graph theory
Secondary: 57M05: Fundamental group, presentations, free differential calculus 05C10: Planar graphs; geometric and topological aspects of graph theory
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 174 , Issue 1 , January 2023 , pp. 199 - 223
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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