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Doubly pointed trisection diagrams and surgery on 2-knots

Published online by Cambridge University Press:  11 August 2021

DAVID GAY  and
JEFFREY MEIER
DAVID GAY
Affiliation:
Euclid Lab, 160 Milledge Terrace, Athens, GA 30606, U.S.A.
JEFFREY MEIER
Affiliation:
Western Washington University, Department of Mathematics, 516 High Street, Bellingham, WA 98225 e-mail: meierj3@www.edu
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Abstract

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We study embedded spheres in 4–manifolds (2–knots) via doubly pointed trisection diagrams, showing that such descriptions are unique up to stabilisation and handleslides, and we describe how to obtain trisection diagrams for certain cut-and-paste operations along 2–knots directly from doubly pointed trisection diagrams. The operations described are classical surgery, Gluck surgery, blowdown, and (±4)–rational blowdown, and we illustrate our techniques and results with many examples.

Keywords

57K45 (Primary)57K40 (Secondary)
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 172 , Issue 1 , January 2022 , pp. 163 - 195
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NCCreative Common License - SA
This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike licence (http://creativecommons.org/licenses/by-nc-sa/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the same Creative Commons licence is included and the original work is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use.
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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