Connected sums of unstabilized Heegaard splittings are unstabilized
نویسندگان
چکیده
Let M1 and M2 be closed, orientable 3–manifolds. Let Hi denote a Heegaard surface in Mi . We prove that if H1#H2 comes from stabilizing a lower genus splitting of M1#M2 then one of H1 or H2 comes from stabilizing a lower genus splitting. This answers a question of C Gordon [9, Problem 3.91]. We also show that every unstabilized Heegaard splitting has a unique expression as the connected sum of Heegaard splittings of prime 3–manifolds.
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