Distance two Heegaard splittings, JS']JSJ decompositions and ranks of 3-manifolds

被引：0
|
作者：
Diao, Wenjie [1 ]
Zou, Yanqing [1 ,2 ]
机构：
[1] East China Normal Univ, Sch Math Sci, Shanghai 200241, Peoples R China
[2] East China Normal Univ, Shanghai Key Lab Pure Math & Math Practice, Shanghai 200241, Peoples R China
来源：
SCIENCE CHINA-MATHEMATICS | 2025年
基金：
中国国家自然科学基金;
关键词：
Heegaard distance; Heegaard genus; rank; hyperbolic; 3-manifold; curve complex; !text type='JS']JS[!/text]J decomposition; GENUS; GEOMETRY; COMPLEX;
D O I：
10.1007/s11425-024-2328-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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).
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页数：12
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