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

Bellettini, Giovanni and Paolini, Giovanni and Paolini, Maurizio and Wang, Yi-Sheng (2022) A table of n-component handlebody links of genus n+1 up to six crossings. Mathematical Proceedings of the Cambridge Philosophical Society . ISSN 0305-0041. doi:10.1017/s0305004122000263. (In Press) https://resolver.caltech.edu/CaltechAUTHORS:20220712-629890000

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1017/S0305004122000263DOIArticle
https://arxiv.org/abs/2003.03748arXivDiscussion Paper
Alternate Title:A table of (n,1)-handlebody links to six crossings
Additional Information:© The Author(s), 2022. Published by Cambridge University Press on behalf of Cambridge Philosophical Society. Received 13 July 2020; revised 04 May 2022; accepted 11 April 2022. Published online by Cambridge University Press: 17 June 2022. The first author benefits from the support of the GNAMPA (Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni) of INdAM (Istituto Nazionale di Alta Matematica). The second author benefits from the support of the Swiss National Science Foundation Professorship grant PP00P2_179110/1. The fourth author gratefully acknowledges the support from National Center of Theoretical Sciences during the preparation of the manuscript.
Funders:
Funding AgencyGrant Number
Istituto Nazionale di Alta Matematica (INdAM)UNSPECIFIED
Swiss National Science Foundation (SNSF)PP00P2_179110/1
National Center of Theoretical SciencesUNSPECIFIED
Classification Code: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
DOI:10.1017/s0305004122000263
Record Number:CaltechAUTHORS:20220712-629890000
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20220712-629890000
Official Citation:BELLETTINI, G., PAOLINI, G., PAOLINI, M., & WANG, Y. (2022). A table of n-component handlebody links of genus n 1 up to six crossings. Mathematical Proceedings of the Cambridge Philosophical Society, 1-25. doi:10.1017/S0305004122000263
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:115518
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:13 Jul 2022 19:00
Last Modified:13 Jul 2022 19:00

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