相关论文: Doubly pointed trisection diagrams and surgery on …

We give diagrammatic algorithms for computing the group trisection, homology groups, and intersection form of a closed, orientable, smooth 4-manifold, presented as a branched cover of a bridge-trisected surface in $\mathbb{S}^{4}$. The…

Iwase and Matsumoto defined `pochette surgery' as a cut-and-paste on 4-manifolds along a 4-manifold homotopy equivalent to $S^2\vee S^1$. The first author in [10] studied infinitely many homotopy 4-spheres obtained by pochette surgery. In…

We present three large families of new examples of plumbed 3-manifolds that bound rational homology 4-balls. These are constructed using two operations, also defined here, that preserve the lack of a lattice embedding obstruction to…

We show that by performing the Gluck twist along the 2-knot $K^2_{pq}$ derived from two ribbon presentations of the ribbon 1-knot $K(p,q)$ we get the standard 4-sphere $S^4$. In the proof we apply Kirby calculus.

In this paper, we study $6$-dimensional GKM manifolds with $4$ fixed points. We classify all possible GKM graphs, and for each type of graph we construct a manifold, proving the existence. We show that six types occur. (P1) complex…

A crucial step in the surgery-theoretic program to classify smooth manifolds is that of representing a middle--dimensional homology class by a smoothly embedded sphere. This step fails even for the simple 4-manifolds obtained from the…

We give a formula for the duality structure of the 3-manifold obtained by doing zero-framed surgery along a knot in the 3-sphere, starting from a diagram of the knot. We then use this to give a combinatorial algorithm for computing the…

In an exploration paper, {\it L. Chen, Algorithms for Deforming and Contracting Simply Connected Discrete Closed Manifolds (I)}, we designed algorithms for deforming and contracting a simply connected discrete closed manifold to a discrete…

We consider the operation to crush a subset of a manifold to one-point when the result of the crushing also be a manifold. Then the Poincare conjecture is split to two problems; for any closed orientable 3-manifold which is not homeomorphic…

We use a triple-point version of the Whitney trick to show that ornaments of three orientable $(2k-1)$-manifolds in $\mathbb R^{3k-1}$, $k>2$, are classified by the $\mu$-invariant. A very similar (but not identical) construction was found…

We construct potentially new manifolds homeomorphic but not diffeomorphic to $\mathbb{CP}^{2} \# 8 \overline{\mathbb{CP}^{2}}$ and $\mathbb{CP}^{2} \# 9 \overline{\mathbb{CP}^{2}}$ via rational blowdown surgery along certain $4$-valent…

The purpose of the present paper is twofold: firstly to extend to non-orientable compact 4-manifolds the notion of gem-induced trisection, directly obtained from colored triangulations (or, equivalently, from colored graphs encoding them,…

Exploiting the affinity between stable generalized complex structures and symplectic structures, we explain how certain constructions coming from symplectic geometry can be performed in the generalized complex setting. We introduce…

We study the geodesic two- and three-point functions of random weighted cubic maps, which are obtained by assigning random edge lengths to random cubic planar maps. Explicit expressions are obtained by taking limits of recently established…

We extend the concepts of trivializing and knotting numbers for knots to spatial graphs and 2-bouquet graphs, in particular. Furthermore, we calculate the trivializing and knotting numbers for projections and pseudodiagrams of 2-bouquet…

Using spinning we analyze in a geometric way Haefliger's smoothly knotted (4k-1)-spheres in the 6k-sphere. Consider the 2-torus standardly embedded in the 3-sphere, which is further standardly embedded in the 6-sphere. At each point of the…

A crown diagram of a smooth, closed oriented 4-manifold can be thought of as the projection of a link in the product of a closed surface and the circle, with chords in the circle direction connecting the strands of each crossing. This paper…

The purpose of this paper is to study geometrically simply-connected homotopy 4-spheres by analyzing $n$-component links with a Dehn surgery realizing $\#^n(S^1\times S^2)$. We call such links $n$R-links. Our main result is that a homotopy…

We prove that all knots with unknotting number at most 21 are smoothly slice in the K3 surface. We also prove a more general statement for 4-manifolds that contain a plumbing tree of spheres. Our strategy is based on a flexible method to…

We approach the cycle double cover conjecture by looking for a circular 2-cell embedding of cubic graphs on an arbitrary surface. It is easy to see that if such an embedding exists, we can get to it from an arbitrary starting 2-cell…