Related papers: Closed surfaces and character varieties

We develop a word mechanism applied in knot and link diagrams for the illustration of a diagrammatic property. We also give a necessary condition for determining incompressible and pairwise incompressible surfaces, that are embedded in knot…

This paper focuses on intersection of closed curves on translation surfaces. Namely, we investigate the question of determining the intersection of two closed curves of a given length on such surfaces. This question has been investigated in…

Based on cluster de-synchronization properties of phase oscillators, we introduce an efficient method for the detection and identification of modules in complex networks. The performance of the algorithm is tested on computer generated and…

We use intersection theory techniques to define an invariant of closed 3-manifolds counting the characters of irreducible representations of the fundamental group in PSL(2,C). We note several properties of the invariant and compute the…

This paper investigates the geometry of canonically polarized surfaces defined over a field of positive characteristic which have a nontrivial global vector field, and the implications that the existence of such surfaces has in the moduli…

We present a systematic geometric framework to study closed quantum systems based on suitably chosen variational families. For the purpose of (A) real time evolution, (B) excitation spectra, (C) spectral functions and (D) imaginary time…

This paper presents multi-font/multi-size Kannada numerals and vowels recognition based on spatial features. Directional spatial features viz stroke density, stroke length and the number of stokes in an image are employed as potential…

We give an account of old and new results concerning many types of non-K\"ahler metrics, with focus on the problem of their coexistence on compact complex manifolds, and their behaviour at deformations and blow-up. We also describe a…

This is a survey paper on algorithms for solving problems in 3-dimensional topology. In particular, it discusses Haken's approach to the recognition of the unknot, and recent variations.

Let X be a smooth complex variety and Y be a closed subvariety of X, or more generally, a closed subscheme of X. We are interested in invariants attached to the singularities of the pair (X, Y). We discuss various methods to construct such…

We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…

Topology is a powerful tool for categorizing magnetization textures by defining a topological index in both two-dimensional (2D) systems, such as thin films or curved surfaces, and in 3D bulk systems. In the emerging field of 3D…

We study incompressible surfaces constructed by Culler-Shalen theory in the context of twisted Alexander polynomials. For a $1$st cohomology class of a $3$-manifold the coefficients of twisted Alexander polynomials induce regular functions…

Let X be a hyperkahler manifold deformation equivalent to a Hilbert scheme of n points on a K3 surface. We compute the graded character formula of the generic Mumford-Tate group representation on the cohomology ring of X, and derive a…

The groups of differential characters of Cheeger and Simons admit a natural multiplicative structure. The map given by the squares of degree 2k differential characters reduces to a homomorphism of ordinary cohomology groups. We prove that…

We use quilted Floer theory to construct functor-valued invariants of tangles arising from moduli spaces of flat bundles on punctured surfaces. As an application, we show the non-triviality of certain elements in the symplectic mapping…

While knotoids on the sphere are well-understood by a variety of invariants, knotoids on the plane have proven more subtle to classify due to their multitude over knotoids on the sphere and a lack of invariants that detect a diagram's…

We construct a set of shape-finders which determine shapes of compact surfaces (iso-density surfaces in galaxy surveys or N-body simulations) without fitting them to ellipsoidal configurations as done earlier. The new indicators arise from…

A natural oriented (2k+2)-chain in CP^{2k+1} with boundary twice RP^{2k+1}, its complex shade, is constructed. Via intersection numbers with the shade, a new invariant, the shade number of k-dimensional subvarieties with normal vector…

We develop a theory of \emph{reduced} Gromov-Witten and stable pair invariants of surfaces and their canonical bundles. We show that classical Severi degrees are special cases of these invariants. This proves a special case of the MNOP…