For any pair of integers g and n with g≥3 and 1≤n≤g,we build a 3-manifold with a distance-2,genus-g Heegaard splitting so that(1)it contains n pairwise disjoint and nonisotopic essential tori;(2)after it is cut ope...For any pair of integers g and n with g≥3 and 1≤n≤g,we build a 3-manifold with a distance-2,genus-g Heegaard splitting so that(1)it contains n pairwise disjoint and nonisotopic essential tori;(2)after it is cut open along these tori,one resulting piece is hyperbolic while the others are small Seifert fibered spaces;(3)it provides a substantial result to the rank versus genus problem.These generalize a result in Qiu and Zou(2019).展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.12131009 and 12326601)Science and Technology Commission of Shanghai Municipality(Grant No.22DZ2229014)。
文摘For any pair of integers g and n with g≥3 and 1≤n≤g,we build a 3-manifold with a distance-2,genus-g Heegaard splitting so that(1)it contains n pairwise disjoint and nonisotopic essential tori;(2)after it is cut open along these tori,one resulting piece is hyperbolic while the others are small Seifert fibered spaces;(3)it provides a substantial result to the rank versus genus problem.These generalize a result in Qiu and Zou(2019).
