Multi-tribrackets

Sam Nelson, Evan Pauletich

Published 2019-03-05Version 1

We introduce multi-tribrackets, algebraic structures for region coloring of diagrams of knots and links with different operations at different kinds of crossings. In particular we consider the case of component multi-tribrackets which have different tribracket operations at single-component crossings and multi-component crossings. We provide examples to show that the resulting counting invariants are generally stronger than the counting invariants associated to the standard tribracket coloring. We reinterpret the results of arXiv:1803.03210 in terms of multi-tribrackets and consider future directions for multi-tribracket theory.