相关论文: Exotic structures and adjunction inequality
We obtain new invariants of topological link concordance and homology cobordism of 3-manifolds from Hirzebruch-type intersection form defects of towers of iterated p-covers. Our invariants can extract geometric information from an arbitrary…
We describe a construction procedure of infinite sets of $2$-links in closed simply connected 4-manifolds that are topologically isotopic, smoothly inequivalent and componentwise topologically unknotted. These 2-links are the first examples…
The main purpose of this article is to classify contact structures on some 3-manifolds, namely lens spaces, most torus bundles over a circle, the solid torus, and the thickened torus T^2 x [0,1]. This classification completes earlier work…
We introduce the concept of pseudo-trisections of smooth oriented compact 4-manifolds with boundary. The main feature of pseudo-trisections is that they have lower complexity than relative trisections for given 4-manifolds. We prove…
We determine topological properties of Stein domains with boundary diffeomorphic to T^3, S^1\times S^2 and some Seifert fibered 3-manifolds.
We describe some natural relations connecting contact geometry, classical Monge-Ampere equations and theory of singularities of solutions to nonlinear PDEs. They reveal the hidden meaning of Monge-Ampere equations and sheds new light on…
We construct infinitely many Legendrian links in the standard contact $\mathbb{R}^3$ with arbitrarily many topologically distinct Lagrangian fillings. The construction is used to find links in $S^3$ that bound topologically distinct pieces…
The physics of charm has become one of the best laboratories exposing the limitations of the naive constituent quark model and also giving hints into a more mature description of meson spectroscopy, beyond the simple quark--antiquark…
We study some classes of semi-linear differential equations including both well-posed and ill-posed cases that can generate cocycles (or cocycle correspondences with generating cocycles). Under exponential dichotomy condition with other…
We consider local geometry of sub-pseudo-Riemannian structures on contact manifolds. We construct fundamental invariants of the structures and show that the structures give rise to Einstein-Weyl geometries in dimension 3, provided that…
We show that any simply connected topological closed $4$-manifold punctured along any compact, totally disconnected tame subset $\Lambda$ admits a continuum of smoothings which are not diffeomorphic to any leaf of a $C^{1,0}$ codimension…
Certain basic inequalities between intrinsic and extrinsic invariants for a submanifold in a (k, m)-contact space form are obtained. As applications we get some results for invariant submanifolds in a (k,m)-contact space form.
In this article, we construct countably many mutually non-isotopic diffeomorphisms of some closed non simply-connected 4-manifolds that are homotopic to but not isotopic to the identity, by surgery along $\Theta$-graphs. As corollaries of…
We show that there exists an exotic pair of $4$-manifolds with boundary whose trisection genera are $4$. We also construct genus-$3$ relative trisections for an infinite family of contractible $4$-manifolds introduced by Akbulut and Kirby.
We classify the real tight contact structures on solid tori up to equivariant contact isotopy and apply the results to the classification of real tight structures on $S^3$ and real lens spaces $L(p,\pm 1)$. We prove that there is a unique…
We give simple characterizations of contact 1-forms in terms of Dirac structures. We also relate normal almost contact structures to the theory of Dirac structures.
Contact structures on 3-manifolds are analyzed by decomposing the manifold along convex surfaces. Background results of Giroux, Eliashberg, Colin, and Honda are discussed with an emphasis on examples. Convex decompositions are then used to…
We argue that topological compactons (solitons with compact support) may be quite common objects if $k$-fields, i.e., fields with nonstandard kinetic term, are considered, by showing that even for models with well-behaved potentials the…
A new topological invariant of closed connected orientable four-dimensional manifolds is proposed. The invariant, constructed via surgery on a special link, is a four-dimensional counterpart of the celebrated SU(2) three-manifold invariant…
A presymplectic structure on odd dimensional manifold is given by a closed 2-form which is nondegenerate, i.e., of maximal rank. We investigate geometry of presymplectic manifolds. Some basic theorems analogous to those in symplectic and…