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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The Kakimizu complex of a connected sum of links


Author: Jessica E. Banks
Journal: Trans. Amer. Math. Soc. 365 (2013), 6017-6036
MSC (2010): Primary 57M25
Published electronically: March 12, 2013
MathSciNet review: 3091274
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Abstract: We show that $ \vert\mathrm {MS}(L_1\char93 L_2)\vert=\vert\mathrm {MS}(L_1)\vert\times \vert\mathrm {MS}(L_2)\vert\times \mathbb{R}$ when $ L_1$ and $ L_2$ are any non-split and non-fibred links. Here $ \mathrm {MS}(L)$ denotes the Kakimizu complex of a link $ L$, which records the taut Seifert surfaces for $ L$. We also show that the analogous result holds if we study incompressible Seifert surfaces instead of taut ones.


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Additional Information

Jessica E. Banks
Affiliation: Mathematical Institute, University of Oxford, 24–29 St Giles’, Oxford OX1 3LB, England
Email: jessica.banks@lmh.oxon.org

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05839-4
PII: S 0002-9947(2013)05839-4
Received by editor(s): October 11, 2011
Received by editor(s) in revised form: March 22, 2012
Published electronically: March 12, 2013
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.