Abstract
We show that | M S ( L 1 # L 2 ) | = | M S ( L 1 ) | × | M S ( L 2 ) | × R |\mathrm {MS}(L_1\# L_2)|=|\mathrm {MS}(L_1)|\times |\mathrm {MS}(L_2)|\times \mathbb {R} when L 1 L_1 and L 2 L_2 are any non-split and non-fibred links. Here M S ( L ) \mathrm {MS}(L) denotes the Kakimizu complex of a link L L , which records the taut Seifert surfaces for L L . We also show that the analogous result holds if we study incompressible Seifert surfaces instead of taut ones.
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