Related papers: Closed surfaces and character varieties

We define an invariant, which we call surface-complexity, of closed 3-manifolds by means of Dehn surfaces. The surface-complexity of a manifold is a natural number measuring how much the manifold is complicated. We prove that it fulfils…

We consider skew ruled surfaces in the three-dimensional Euclidean space and some geometrically distinguished families of curves on them whose normal curvature has a concrete form. The aim of this paper is to find and classify all ruled…

We give an effective characterisation of the walls in the variation of geometric invariant theory problem associated to a quiver and a dimension vector.

It is given the diffeomorphism classification on generic singularities of tangent varieties to curves with arbitrary codimension in a projective space. The generic classifications are performed in terms of certain geometric structures and…

This article finds constant scalar curvature Kahler metrics on certain compact complex surfaces. The surfaces considered are those admitting a holomorphic submersion to a curve, with fibres of genus at least 2. The proof is via an adiabatic…

We show that when a K3 surface acquires a node, the existence of stable spherical sheaves of certain Chern classes can be obstructed.

We discuss methods to construct a polynomial parametrization of some interesting knotted surfaces (knotted spheres, knotted tori and knotted planes) and provide examples.

Given a closed four-manifold $X$ with an indefinite intersection form, we consider smoothly embedded surfaces in $X \setminus $int$(B^4)$, with boundary a knot $K \subset S^3$. We give several methods to bound the genus of such surfaces in…

Moduli spaces of stable sheaves on smooth projective surfaces are in general singular. Nonetheless, they carry a virtual class, which -- in analogy with the classical case of Hilbert schemes of points -- can be used to define intersection…

This study defines finite-type invariants for curves on surfaces and reveals the construction of these finite-type invariants for stable homeomorphism classes of curves on compact oriented surfaces without boundaries. These invariants are a…

We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs.…

We consider closed acylindrical surfaces in 3-manifolds and in knot and link complements, and show that the genus of these surfaces is bounded linearly by the number of tetrahedra in the triangulation of the manifold and by the number of…

In this study, we give the dual characterizations of Mannheim offsets of the ruled surface in terms of their integral invariants and the new characterization of the Mannheim offsets of developable surface. Furthermore, we obtain the…

Indices of vector fields on (complex analytic) singular varieties have been considered by various authors from several different viewpoints. All these indices coincide with the classical local index of Poincar\'e-Hopf when the ambient…

For each $k\in\mathbb{A}^4(\mathbb{C})$, consider the character variety $X_k$ on a four-holed sphere. We prove that it is decidable whether or not any two integral solutions of $X_k$ are in the same mapping class group orbit. For this,…

We give a classification of compact solitons for the pluriclosed flow on complex surfaces. First, by exploiting results from the Kodaira classification of surfaces, we show that the complex surface underlying a soliton must be K\"ahler…

The Kreck-Stolz s invariant is used to distinguish connected components of the moduli space of positive scalar curvature metrics. We use a formula of Kreck and Stolz to calculate the s invariant for metrics on S^n bundles with nonnegative…

J.H.C. Whitehead introduced the concept of crossed modules in the early 20th century. These crossed modules are crucial for algebraic models of 2-type homotopy, which involve connected spaces with no higher than second-degree homotopy…

We compute the transgressed forms of some modularly invariant characteristic forms,which are related to the twisted elliptic genera. We study the modularity properties of these secondary characteristic forms and relations among them. We…

Cluster varieties are geometric objects that have recently found applications in several areas of mathematics and mathematical physics. This thesis studies the geometry of a large class of cluster varieties associated to compact oriented…