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

 

Towards invariants of surfaces in $ 4$-space via classical link invariants


Author: Sang Youl Lee
Journal: Trans. Amer. Math. Soc. 361 (2009), 237-265
MSC (2000): Primary 57Q45; Secondary 57M25
Published electronically: August 13, 2008
MathSciNet review: 2439406
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Abstract: In this paper, we introduce a method to construct ambient isotopy invariants for smooth imbeddings of closed surfaces into $ 4$-space by using hyperbolic splittings of the imbedded surfaces and an arbitrary given isotopy or regular isotopy invariant of classical knots and links in $ 3$-space. Using this construction, adopting the Kauffman bracket polynomial as an example, we produce some invariants.


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Additional Information

Sang Youl Lee
Affiliation: Department of Mathematics, Pusan National University, Pusan 609-735, Korea
Email: sangyoul@pusan.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04568-6
PII: S 0002-9947(08)04568-6
Keywords: Kauffman bracket polynomial, knotted surface, knot with bands, surface link, Yoshikawa moves, ch-diagram
Received by editor(s): December 18, 2006
Published electronically: August 13, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.