Related papers: Orientations complexes des J-courbes reelles
Suppose $S$ is a closed, oriented surface of genus at least two. This paper investigates the geometry of the homology multicurve complex, $\mathcal{HC}(S,\alpha)$, of $S$; a complex closely related to complexes studied by…
The Castelnuovo-Mumford regularity of the Jacobian algebra and of the graded module of derivations associated to a general curve arrangement in the complex projective plane are studied. The key result is an addition-deletion type result,…
Jacques Tits gave a general recipe for producing an abstract geometry from a semisimple algebraic group. This expository paper describes a uniform method for giving a concrete realization of Tits's geometry and works through several…
The homology of Kontsevich's commutative graph complex parameterizes finite type invariants of odd dimensional manifolds. This {\it graph homology} is also the twisted homology of Outer Space modulo its boundary, so gives a nice point of…
We show that on a Kahler manifold whether the J-flow converges or not is independent of the chosen background metric in its Kahler class. On toric manifolds we give a numerical characterization of when the J-flow converges, verifying a…
We prove the existence of primitive curves and positivity of intersections of $J$-complex curves for Lipschitz-continuous almost complex structures. These results are deduced from the Comparison Theorem for $J$-holomorphic maps in Lipschitz…
Through the means of an alternative and less algebraic method, an explicit expression for the isometry groups of the six-dimensional homogeneous nearly K\"ahler manifolds is provided.
Answering connectivity queries in real algebraic sets is a fundamental problem in effective real algebraic geometry that finds many applications in e.g. robotics where motion planning issues are topical. This computational problem is…
We review some cohomological aspects of complex and hypercomplex manifolds and underline the differences between both realms. Furthermore, we try to highlight the similarities between compact complex surfaces on one hand and compact…
We extend the Newlander-Nirenberg theorem to manifolds with almost complex structures that have somewhat less than Lipschitz regularity. We also discuss the regularity of local holomorphic coordinates in the integrable case, with particular…
The paper is devoted to the problem when a map from some closed connected manifold to an aspherical closed manifold approximately fibers, i.e., is homotopic to Manifold Approximate Fibration. We define obstructions in algebraic K-theory.…
Real algebraic geometry is the study of semi-algebraic sets, subsets of $\R^k$ defined by Boolean combinations of polynomial equalities and inequalities. The focus of this thesis is to study quantitative results in real algebraic geometry,…
In [5], without giving a detailed proof, Yamauchi provided a formula to calculate the genus of a certain family of smooth complete intersection algebraic curves. That formula is used extensively in [1] to study the algebraic curves for…
The goal of this work is to establish a proof of the Gromov convergence in Hoelder spaces for curves with a totally real boundary condition following the original geometric idea of Gromov. We use a local reflection principle in…
This paper explores recent progress related to constraint maps. Building on the exposition in [14], our goal is to provide a clear and accessible account of some of the more intricate arguments behind the main results in this work. Along…
Quasiconformal maps in the complex plane are homeomorphisms that satisfy certain geometric distortion inequalities; infinitesimally, they map circles to ellipses with bounded eccentricity. The local distortion properties of these maps give…
We investigate the orientability of a class of vector bundles over flag manifolds of real semi-simple Lie groups, which include the tangent bundle and also stable bundles of certain gradient flows. Closed formulas, in terms of roots, are…
These notes present a systematic treatment of local properties of J-holomorphic maps and of Gromov's convergence for sequences of such maps, specifying the assumptions needed for all statements. In particular, only one auxiliary statement…
A linear constraint is given on the Betti numbers of a compact hyper-Kaehler manifold, using an index formula for c_1c_{n-1} on an almost complex manifold. The topology of some other manifolds with reduced holonomy is also discussed…
We introduce the concept of a topological J-group and determine for many important examples of topological groups if they are topological J-groups or not. Besides other results, we show that the underlying topological space of a pathwise…