On calculating the slice genera of 11- and 12-crossing knots

Lewark, Lukas; McCoy, Duncan (2019). On calculating the slice genera of 11- and 12-crossing knots. Experimental mathematics, 28(1), pp. 81-94. Taylor & Francis 10.1080/10586458.2017.1353453

[img] Text
Lewark McCoy - On calculating the slice genera of 11- and 12-crossing knots - Exp Math.pdf - Published Version
Restricted to registered users only
Available under License Publisher holds Copyright.

Download (689kB) | Request a copy
[img]
Preview
Text
1508.01098.pdf - Submitted Version
Available under License Publisher holds Copyright.

Download (436kB) | Preview

This article contains the results of efforts to determine the values of the smooth and the topological slice genus of 11- and 12-crossing knots. Upper bounds for these genera were produced by using a computer to search for genus one concordances between knots. For the topological slice genus, further upper bounds were produced using the algebraic genus. Lower bounds were obtained using a new obstruction from the Seifert form and by the use of Donaldson’s diagonalization theorem. These results complete the computation of the topological slice genera for all knots with at most 11 crossings and leaves the smooth genera unknown for only two 11-crossing knots. For 12 crossings, there remain merely 25 knots whose smooth or topological slice genus is unknown.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Lewark, Lukas Pascal

Subjects:

500 Science > 510 Mathematics

ISSN:

1058-6458

Publisher:

Taylor & Francis

Language:

English

Submitter:

Michel Arthur Bik

Date Deposited:

17 Feb 2020 15:02

Last Modified:

17 Feb 2020 15:02

Publisher DOI:

10.1080/10586458.2017.1353453

ArXiv ID:

1508.01098

BORIS DOI:

10.7892/boris.139953

URI:

https://boris.unibe.ch/id/eprint/139953

Actions (login required)

Edit item Edit item
Provide Feedback