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
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
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
Letπ=π_(1)(M)for a compact 3-manifold M,andχ_(4),p and q^(*)be the invariants of Hausmann and Weinberger(1985),Kotschick(1994)and Hillman(2002),respectively.For a certain class of compact 3-manifolds M,including al...Letπ=π_(1)(M)for a compact 3-manifold M,andχ_(4),p and q^(*)be the invariants of Hausmann and Weinberger(1985),Kotschick(1994)and Hillman(2002),respectively.For a certain class of compact 3-manifolds M,including all those not containing two-sided RP2’s,we determineχ_(4)(π).We address when p(π)equalsχ_(4)(π)and when q^(*)(π)equalsχ_(4)(π),and answer a question raised by Hillman(2002).展开更多
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.
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.
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 Simons Collaborations in Mathematics and the Physical Sciences(Grant No.615229).
文摘Letπ=π_(1)(M)for a compact 3-manifold M,andχ_(4),p and q^(*)be the invariants of Hausmann and Weinberger(1985),Kotschick(1994)and Hillman(2002),respectively.For a certain class of compact 3-manifolds M,including all those not containing two-sided RP2’s,we determineχ_(4)(π).We address when p(π)equalsχ_(4)(π)and when q^(*)(π)equalsχ_(4)(π),and answer a question raised by Hillman(2002).
