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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Towards invariants of surfaces in $4$-space via classical link invariants
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by Sang Youl Lee PDF
Trans. Amer. Math. Soc. 361 (2009), 237-265 Request permission

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
  • Received by editor(s): December 18, 2006
  • Published electronically: August 13, 2008
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 361 (2009), 237-265
  • MSC (2000): Primary 57Q45; Secondary 57M25
  • DOI: https://doi.org/10.1090/S0002-9947-08-04568-6
  • MathSciNet review: 2439406