The Kakimizu complex of a connected sum of links

Abstract

We show that $|MS(L_1 # L_2)|=|MS(L_1)|\times|MS(L_2)|\times\mathbb{R}$ when $L_1$ and $L_2$ are any non-split and non-fibred links. Here $MS(L)$ denotes the Kakimizu complex of a link $L$, which records the taut Seifert surfaces for $L$. We also show that the analogous result holds if we study incompressible Seifert surfaces instead of taut ones.

arXiv comment23 pages, 8 figures. This result has been proved independently by Bassem Saad

References in corpus (1)

• Contractibility of the Kakimizu complex and symmetric Seifert surfaces

Cited by in corpus (4)

• The coarse geometry of the Kakimizu complex
• The Kakimizu complex of a surface
• The Kakimizu complex of a split link
• The quasi-isomorphism class of the Kakimizu complex