Title  Ideal coset invariants for surfacelinks in $mathbb R^4$. 
Author(s)  Yewon Joung, Jieon Kim, Sang Youl Lee 
Type  Article in Journal 
Abstract  In [Towards invariants of surfaces in 4space via classical link invariants, Trans. Amer. Math. Soc.361 (2009) 237–265], Lee defined a polynomial [[D]] for marked graph diagrams D of surfacelinks in 4space by using a statesum model involving a given classical link invariant. In this paper, we deal with some obstructions to obtain an invariant for surfacelinks represented by marked graph diagrams D by using the polynomial [[D]] and introduce an ideal coset invariant for surfacelinks, 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.

Keywords  Chdiagram; marked graph diagram; knotted surface; surfacelink; invariant of surfacelink; state–sum model; Kauffman bracket polynomial; Gröbner basis; Yoshikawa move 
ISSN  02182165; 17936527/e 
URL 
http://www.worldscientific.com/doi/abs/10.1142/S0218216513500521 
Language  English 
Journal  J. Knot Theory Ramifications 
Volume  22 
Number  9 
Pages  25 
Publisher  World Scientific, Singapore 
Year  2013 
Edition  0 
Translation 
No 
Refereed 
No 