Extending the Classical Skein

摘要: We summarize the theory of a new skein invariant classical links H[H] that generalizes regular isotopy version Homflypt polynomial, H. The is based on procedure where we apply relation only to crossings distinct components, so as produce collections unlinked knots and then evaluate resulting using H inserting at same time parameter. This procedure, remarkably, leads generalization but also generalizations other known invariants, such Kauffman polynomial. discuss different approaches link H[H], algebraic one related its ambient equivalent \(\Theta \), skein-theoretic reformulation into summation generating sublinks given link. finally give examples illustrating behaviour further research directions possible application areas.