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355 (2003), no. 10, 3947–3989. 4. ” Encyclopaedia of Mathematical Sciences, 142. Low-Dimensional Topology, III. Springer-Verlag, Berlin, 2004. 5. D. QA/0409602. March 4, 2007 11:41 WSPC - Proceedings Trim Size: 9in x 6in ws-procs9x6 17 6. , Racks and links in codimension two, Journal of Knot Theory and Its Ramifications Vol. 1 No. 4 (1992), 343–406. 7. R. Fenn, C. Rourke, and B. uk/~bjs/ 8. , A classifying invariant of knots, the knot quandle, J. Pure Appl. Alg. 23, 37–65. 9. Majid, S. ” London Mathematical Society Lecture Note Series, 292.

1, 78–88, 160. 11. , Abstraction of symmetric Transformations: Introduction to the Theory of kei, Tohoku Math. J. 49, (1943). 145–207 (a recent translation by Seiichi Kamada is available from that author). March 4, 2007 11:41 WSPC - Proceedings Trim Size: 9in x 6in This page intentionally left blank ws-procs9x6 March 28, 2007 12:37 WSPC - Proceedings Trim Size: 9in x 6in ws-procs9x6 Intelligence of Low Dimensional Topology 2006 Eds. J. Scott Carter et al. (pp. 19–25) c 2007 World Scientific Publishing Co.

Introduction Khovanov homology is an invariant of links which was introduced by M. 5 The most basic feature of this link invariant is that it dominates the Jones polynomial. e. 3 Since its discovery, Khovanov homology has been subject to extensive literature. For instance, there were various attempts to simplify Khovanov’s construction and to generalize it into several directions. In particular, Viro8 introduced a combinatorial definition of the Khovanov chain complex. Viro’s elementary construction plays a key role in our paper.

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