Abstract
Let V∪ S W be a reducible Heegaard splitting of genus g = g(S) ⩾ 2. For a maximal prime connected sum decomposition of V ∪ S W, let q denote the number of the genus 1 Heegaard splittings of S 2 × S 1 in the decomposition, and p the number of all other prime factors in the decomposition. The main result of the present paper is to describe the relation of p, q and dim(C V ∩ C W ).
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Sun, D., Lei, F. & Li, F. On reducible Heegaard splittings. Sci. China Math. 56, 221–226 (2013). https://doi.org/10.1007/s11425-012-4548-y
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DOI: https://doi.org/10.1007/s11425-012-4548-y