UC Davis

We discuss the development of the Kakimizu complex as well as the mathematical techniquesthat have been developed to study it. By using these techniques we determine the Kakimizu complex for a new class of links which are the result of plumbing an n-times full twisted band, n ≥ 2 to a Seifert surface for a special alternating link. We also show how the maximal simplices of the Kakimizu complex for the resulting link can be directly obtained from the maximal simplices of the original special alternating link.