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TitleIdeal coset invariants for surface-links in $mathbb R^4$.
Author(s) Yewon Joung, Jieon Kim, Sang Youl Lee
TypeArticle in Journal
AbstractIn [Towards invariants of surfaces in 4-space via classical link invariants, Trans. Amer. Math. Soc.361 (2009) 237–265], Lee defined a polynomial [[D]] for marked graph diagrams D of surface-links in 4-space by using a state-sum model involving a given classical link invariant. In this paper, we deal with some obstructions to obtain an invariant for surface-links represented by marked graph diagrams D by using the polynomial [[D]] and introduce an ideal coset invariant for surface-links, which is defined to be the coset of the polynomial [[D]] in a quotient ring of a certain polynomial ring modulo some ideal and represented by a unique normal form, i.e. a unique representative for the coset of [[D]] that can be calculated from [[D]] with the help of a Gröbner basis package on computer.

KeywordsCh-diagram; marked graph diagram; knotted surface; surface-link; invariant of surface-link; state–sum model; Kauffman bracket polynomial; Gröbner basis; Yoshikawa move
ISSN0218-2165; 1793-6527/e
URL http://www.worldscientific.com/doi/abs/10.1142/S0218216513500521
JournalJ. Knot Theory Ramifications
PublisherWorld Scientific, Singapore
Translation No
Refereed No