Murasugi sum of $${\varvec{k}}$$ k –open books

A k–open book of a closed n–manifold X is a way to express X as a fiber bundle $$\pi : X\setminus B \rightarrow S^k$$ π : X \ B → S k over the k–sphere $$S^k$$ S k in the complement of a $$(n-k-1)$$ ( n - k - 1 ) –dimensional submanifold B of X. One can associate an abstract k–open book to a given k–open book of a closed manifold. Given an abstract k–open book of a closed manifold X and an abstract k–open book of a closed manifold $$X^\prime $$ X ′ , we define the notion of their Murasugi sum and show that the closed manifold associated to the Murasugi sum is the connected sum of X and $$X^\prime $$ X ′ .