In this paper, we establish a rigidity theorem for compact constant mean curva- ture surfaces of the Berger sphere in terms of the surfaces＇ geometric invariants. This extends the previous similar result on compact m...In this paper, we establish a rigidity theorem for compact constant mean curva- ture surfaces of the Berger sphere in terms of the surfaces＇ geometric invariants. This extends the previous similar result on compact minimal surfaces of the Berger sphere.展开更多
In this paper, I give out an algorithm of the witten' s invariants of the 3-manifolds obtained by surgery on the links whose corresponding graphs may be no longer trees.
Let H be a handlebody, J={J 1, …, J n} a collection of 2 sided pairwise disjoint simple closed curves on H. The 3 manifold obtained from H by attaching 2 handles to H along the curves in J is called an n re...Let H be a handlebody, J={J 1, …, J n} a collection of 2 sided pairwise disjoint simple closed curves on H. The 3 manifold obtained from H by attaching 2 handles to H along the curves in J is called an n relator 3 manifold, and is denoted as H J. In this paper, a sufficient and necessary condition for H J to be a handlebody is described.展开更多
An essential annulus A properly imbedded in a 3-manifold M is said to be spanning with respect to a Hereaard splitting VUFW of M if the two components of A are lying in A and separately and A intersects the Heegaard s...An essential annulus A properly imbedded in a 3-manifold M is said to be spanning with respect to a Hereaard splitting VUFW of M if the two components of A are lying in A and separately and A intersects the Heegaard surface F in one circle. In this paper,a sufficient and necessary condition that there is a spanning annulus A in a 3-manifold M with respect to the Heegaard splitting VUFW is given.展开更多
In this paper,the authors give some sufficient conditions for an amalgamated 3-manifold along a compact connected surface F with boundary to be ∂-irreducible in terms of distances between some kinds of vertex subsets ...In this paper,the authors give some sufficient conditions for an amalgamated 3-manifold along a compact connected surface F with boundary to be ∂-irreducible in terms of distances between some kinds of vertex subsets of the curve complex and the arc complex of F.展开更多
By constructing certain maps, this note completes the answer of the question： For which closed orientable 3-manifold N, is the set of mapping degrees D（M, N） finite for any closed orientable 3-manifold M？
文摘In this paper, we establish a rigidity theorem for compact constant mean curva- ture surfaces of the Berger sphere in terms of the surfaces＇ geometric invariants. This extends the previous similar result on compact minimal surfaces of the Berger sphere.
文摘In this paper, I give out an algorithm of the witten' s invariants of the 3-manifolds obtained by surgery on the links whose corresponding graphs may be no longer trees.
文摘Let H be a handlebody, J={J 1, …, J n} a collection of 2 sided pairwise disjoint simple closed curves on H. The 3 manifold obtained from H by attaching 2 handles to H along the curves in J is called an n relator 3 manifold, and is denoted as H J. In this paper, a sufficient and necessary condition for H J to be a handlebody is described.
文摘An essential annulus A properly imbedded in a 3-manifold M is said to be spanning with respect to a Hereaard splitting VUFW of M if the two components of A are lying in A and separately and A intersects the Heegaard surface F in one circle. In this paper,a sufficient and necessary condition that there is a spanning annulus A in a 3-manifold M with respect to the Heegaard splitting VUFW is given.
基金supported by the National Natural Science Foundation of China(No.12071051)。
文摘In this paper,the authors give some sufficient conditions for an amalgamated 3-manifold along a compact connected surface F with boundary to be ∂-irreducible in terms of distances between some kinds of vertex subsets of the curve complex and the arc complex of F.
基金The third author is partially supported by National Natural Science Foundation of China （Grant No. 10631060） and Ph.D. grant of the Ministry of Education of China （Grant No. 5171042-055）
文摘By constructing certain maps, this note completes the answer of the question： For which closed orientable 3-manifold N, is the set of mapping degrees D（M, N） finite for any closed orientable 3-manifold M？
