We show that |MS(L_1 # L_2)|=|MS(L_1)|\times|MS(L_2)|\times\mathbb{R} when
L1β and L2β 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.Comment: 23 pages, 8 figures. This result has been proved independently by
Bassem Saa