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

Abhijeet Ghanwat (), Suhas Pandit () and Selvakumar A. ()
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Abhijeet Ghanwat: Tata Institute of Fundamental Research
Suhas Pandit: Indian Institute of Technology Madras
Selvakumar A.: The Institute of Mathematical Sciences, Chennai

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 1, 266-272

Abstract: Abstract 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 ′ .

Keywords: Manifolds; k–open books; Open books; Primary: 57R45; 57R15; 57R65 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-023-00477-0

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