Let （M1, M2, N） be three symplectic manifolds and suppose that we can do the symplectic connected sum of M1 and M2 along their submanifold N to obtain M1^#NM2. In this paper, we consider the bilinear and cubic forms...Let （M1, M2, N） be three symplectic manifolds and suppose that we can do the symplectic connected sum of M1 and M2 along their submanifold N to obtain M1^#NM2. In this paper, we consider the bilinear and cubic forms of H＊（M1^#NM2, Z） when dimM1^#NM2 = 4, 6. Under some conditions, we get some relations of the bilinear and the cubic forms between M1^#NM2 and M1 [I Ms.展开更多
The connected sum is a fundamental operation in geometric topology and combinatorics.In this paper,we study the connection between connected sums of simplicial spheres and the algebraic topology of their corresponding...The connected sum is a fundamental operation in geometric topology and combinatorics.In this paper,we study the connection between connected sums of simplicial spheres and the algebraic topology of their corresponding moment-angle manifolds.The cohomology rings of moment-angle manifolds corresponding to connected sums of simplicial spheres are computed,which leads to a conjecture on the topology of such moment-angle manifolds.展开更多
In this paper, we compute Atom-bond connectivity index, Fourth atom-bond connectivity index, Sum connectivity index, Randic connectivity index, Geometric-arithmetic connectivity index and Fifth geometric-arithmetic co...In this paper, we compute Atom-bond connectivity index, Fourth atom-bond connectivity index, Sum connectivity index, Randic connectivity index, Geometric-arithmetic connectivity index and Fifth geometric-arithmetic connectivity index of Dutch windmill graph.展开更多
In this paper, we shall prove that any Heegaard splitting of a δ-reducible 3-manifold M, say M = W U V, can be obtained by doing connected sums, boundary connected sums and self-boundary connected sums from Heegaard ...In this paper, we shall prove that any Heegaard splitting of a δ-reducible 3-manifold M, say M = W U V, can be obtained by doing connected sums, boundary connected sums and self-boundary connected sums from Heegaard splittings of n manifolds M1,..., Mn, where Mi is either a solid torus or an irreducible, δ-irreducible manifold.展开更多
Let W be a closed area enlargeable manifold in the sense of Gromov-Lawson and M be a noncompact spin manifold,the authors show that the connected sum M#W admits no complete metric of positive scalar curvature.When W=T...Let W be a closed area enlargeable manifold in the sense of Gromov-Lawson and M be a noncompact spin manifold,the authors show that the connected sum M#W admits no complete metric of positive scalar curvature.When W=T^(n),this provides a positive answer to the generalized Geroch conjecture in the spin setting.展开更多
For a generic anti-canonical hypersurface in each smooth toric Fano 4-fold with rank 2 Picard group, we prove there exist three isolated rational curves in it. Moreover, for all these 4-folds except one, the contracti...For a generic anti-canonical hypersurface in each smooth toric Fano 4-fold with rank 2 Picard group, we prove there exist three isolated rational curves in it. Moreover, for all these 4-folds except one, the contractions of generic anti-canonical hypersurfaces along the three rational curves can be deformed to smooth threefolds which is diffeomorphic to connected sums of S3 ~ S~. In this manner, we obtain complex structures with trivial canonical bundles on some connected sums of S^3 × S^3. This construction is an analogue of that made by Friedman [On threefolds with trivial canonical bundle. In： Complex Geometry and Lie Theory, volume 53 of Proc. Sympos. Pure Math., Amer. Math. Soc., Providence, RI, 1991, 103-134], Lu and Tian [Complex structures on connected sums of S^3× S^3. In： Manifolds and Geometry, Pisa, 1993, 284 293] who used only quintics in P^4.展开更多
An equivalent description for the torus knot is given in this paper, and the classification theorem of the torus knot is proved in an elementary method. Using the circular presentation of torus knot , we showed that t...An equivalent description for the torus knot is given in this paper, and the classification theorem of the torus knot is proved in an elementary method. Using the circular presentation of torus knot , we showed that the genus of the torus knot Kp,q is 1/2（p-1）（q-1） A knot called as bitorus knot is defined in the paper and showed . special that bitorus knot are all the connected sum of two torus knots.展开更多
文摘Let （M1, M2, N） be three symplectic manifolds and suppose that we can do the symplectic connected sum of M1 and M2 along their submanifold N to obtain M1^#NM2. In this paper, we consider the bilinear and cubic forms of H＊（M1^#NM2, Z） when dimM1^#NM2 = 4, 6. Under some conditions, we get some relations of the bilinear and the cubic forms between M1^#NM2 and M1 [I Ms.
基金supported by National Natural Science Foundation of China(Grant Nos.11801580 and 11871284)supported by National Natural Science Foundation of China(Grant Nos.11871284 and 11761072).
文摘The connected sum is a fundamental operation in geometric topology and combinatorics.In this paper,we study the connection between connected sums of simplicial spheres and the algebraic topology of their corresponding moment-angle manifolds.The cohomology rings of moment-angle manifolds corresponding to connected sums of simplicial spheres are computed,which leads to a conjecture on the topology of such moment-angle manifolds.
基金Supported by the National 973 Plan project(2011CB706900)the National 863 Plan project(2011AA01A102)+1 种基金the NSFC(11331012,11571015)the "Strategic Priority Research Program" of Chinese Academy of Sciences(XDA06010302)
文摘In this paper, we compute Atom-bond connectivity index, Fourth atom-bond connectivity index, Sum connectivity index, Randic connectivity index, Geometric-arithmetic connectivity index and Fifth geometric-arithmetic connectivity index of Dutch windmill graph.
基金the National Natural Science Foundation of China (10171024, 10171038)
文摘In this paper, we shall prove that any Heegaard splitting of a δ-reducible 3-manifold M, say M = W U V, can be obtained by doing connected sums, boundary connected sums and self-boundary connected sums from Heegaard splittings of n manifolds M1,..., Mn, where Mi is either a solid torus or an irreducible, δ-irreducible manifold.
基金supported by the National Natural Science Foundation of China(Nos.11931007,12101361)the Nankai Zhide Foundationthe project of Young Scholars of SDU and the Fundamental Research Funds of SDU(No.2020GN063)。
文摘Let W be a closed area enlargeable manifold in the sense of Gromov-Lawson and M be a noncompact spin manifold,the authors show that the connected sum M#W admits no complete metric of positive scalar curvature.When W=T^(n),this provides a positive answer to the generalized Geroch conjecture in the spin setting.
文摘For a generic anti-canonical hypersurface in each smooth toric Fano 4-fold with rank 2 Picard group, we prove there exist three isolated rational curves in it. Moreover, for all these 4-folds except one, the contractions of generic anti-canonical hypersurfaces along the three rational curves can be deformed to smooth threefolds which is diffeomorphic to connected sums of S3 ~ S~. In this manner, we obtain complex structures with trivial canonical bundles on some connected sums of S^3 × S^3. This construction is an analogue of that made by Friedman [On threefolds with trivial canonical bundle. In： Complex Geometry and Lie Theory, volume 53 of Proc. Sympos. Pure Math., Amer. Math. Soc., Providence, RI, 1991, 103-134], Lu and Tian [Complex structures on connected sums of S^3× S^3. In： Manifolds and Geometry, Pisa, 1993, 284 293] who used only quintics in P^4.
文摘An equivalent description for the torus knot is given in this paper, and the classification theorem of the torus knot is proved in an elementary method. Using the circular presentation of torus knot , we showed that the genus of the torus knot Kp,q is 1/2（p-1）（q-1） A knot called as bitorus knot is defined in the paper and showed . special that bitorus knot are all the connected sum of two torus knots.
