相关论文: Slope inequalities for fibred surfaces via GIT

Meier and Zupan showed that every surface in the four-sphere admits a bridge trisection and can therefore be represented by three simple tangles. This raises the possibility of applying methods from link homology to knotted surfaces. We use…

In this paper, we introduce the notion of generalized squeezing function and study the basic properties of generalized squeezing functions and Fridman invariants. We also study the comparison of these two invariants, in terms of the…

We show that a holomorphic two-form $\theta$ on a smooth algebraic variety X localizes the virtual fundamental class of the moduli of stable maps $\mgn(X,\beta)$ to the locus where $\theta$ degenerates; it then enables us to define the…

We present a new invariant, called slope, of a colored link in an integral homology sphere and use this invariant to complete the signature formula for the splice of two links. We develop a number of ways of computing the slope and a few…

In this note we introduce a natural Finsler structure on convex surfaces, referred to as the projective Finsler structure, which is dual in a sense to the obvious inclusion of a convex surface in a normed space. It has an associated…

In this paper we will explore a way to prove the hundred years old Gronwall's conjecture: if two plane linear 3-webs with non-zero curvature are locally isomorphic, then the isomorphism is a homography. Using recent results of S. I.…

The chapter contains a detailed presentation of the surface integral theory for modelling light diffraction by surface-relief diffraction gratings having a one-dimensional periodicity. Several different approaches are presented, leading…

We study geometry of curves passing through a Whitney umbrella by using a Darboux frame along it. We define three invariants by using Frenet-Serre type formula relating to the geodesic curvature, the normal curvature, and the geodesic…

We give a new differential-geometric proof of Grauert's theorem on the coherence of the higher direct image of a coherent sheaf under a proper holomorphic morphism between complex analytic spaces. In the smooth case, our approach is based…

In this paper we study embeddings of oriented connected closed surfaces in $\mathbb S^3$. We define a complete invariant, the fundamental span, for such embeddings, generalizing the notion of the peripheral system of a knot group. From the…

We introduce an invariant for trivalent fatgraph spines of a once bordered surface, which takes values in the first homology of the surface. This invariant is the secondary object coming from two 1-cocycles on the dual fatgraph complex, one…

We give a proof of the Jardine-Tillmann generalized group completion theorem. It is much in the spirit of the original homology fibration approach by McDuff and Segal, but follows a modern treatment of homotopy colimits, using as little…

We introduce invariants of spatial graphs related to the Wu invariant and the Simon invariant, and apply them to prove that certain graphs are intrinsically chiral, and to obtain lower bounds for the minimal crossing number of embedded…

This article describes the use of symplectic cut-and-paste methods to compute Gromov-Witten invariants. Our focus is on recent advances extending these methods to Kahler surfaces with geometric genus p_g>0, for which the usual GW invariants…

We classify quartic del Pezzo surface fibrations over the projective line via numerical invariants, giving explicit examples for small values of the invariants. For generic such fibrations, we describe explicitly the geometry of spaces of…

We prove a surface embedding theorem for 4-manifolds with good fundamental group in the presence of dual spheres, with no restriction on the normal bundles. The new obstruction is a Kervaire-Milnor invariant for surfaces and we give a…

We prove a quantum version of Kalkman's wall-crossing formula comparing Gromov-Witten invariants on geometric invariant theory (git) quotients related by a change in polarization. The wall-crossing terms are gauged Gromov-Witten invariants…

We use topological methods to study various semicontinuity properties of spectra of singular points of plane algebraic curves and of polynomials in two variables at infinity. Using Seifert forms and the Tristram--Levine signatures of links,…

We introduce defects, with internal gauge symmetries, on a knot and Seifert surface to a knot into the combinatorial construction of finite gauge-group Dijkgraaf-Witten theory. The appropriate initial data for the construction are certain…

Machine learning models that are developed with invariance to certain types of data transformations have demonstrated superior generalization performance in practice. However, the underlying mechanism that explains why invariance leads to…