Related papers: An example of a domain in a complex flag manifold
We study the approximation of J-holomorphic maps continuous to the boundary from ma domain in the complex plane into an almost complex manifold by maps J-holomorphic to the boundary, giving partial results in the non-integrable case. For…
We consider properties and applications of a compact, Hausdorff topology called the "ultrafilter topology" defined on an {\sl arbitrary spectral space} and we observe that this topology coincides with the constructible topology. If $K$ is a…
This is a study on approximating a Riemannian manifold by polyhedra. Our scope is understanding Tullio Regge's [52] article in the restricted Riemannian frame. We give a proof of the Regge theorem along lines close to its original…
We prove the existence of multiple closed geodesics on non-compact cylindrica manifolds.
In the current article our primary objects of study are compact complex submanifolds of quotient manifolds of irreducible bounded symmetric domains by torsion free discrete lattices of automorphisms. We are interested in the…
The purpose of this note is to define tri-moment maps for certain manifolds that carry closed non-degenerate 4-forms and an $Sp(1)^n$-action. Examples include quaternionic vector spaces and flag manifolds. We show how this map can be used…
This paper advocates a novel framework for segmenting a dataset in a Riemannian manifold $M$ into clusters lying around low-dimensional submanifolds of $M$. Important examples of $M$, for which the proposed clustering algorithm is…
Given a complex manifold containing a relatively compact $Z(q)$ domain, we give sufficient geometric conditions on the domain so that its $L^2$-cohomology in degree $(p,q)$ (known to be finite dimensional) vanishes. The condition consists…
A classical problem of mechanics involves a projectile fired from a given point with a given velocity whose direction is varied. This results in a family of trajectories whose envelope defines the border of a 'safe' domain. In the simple…
In this paper, we present a closed, computable formula for the cellular homology coefficients of real flag manifolds associated with split real forms of type A. We demonstrate the process using movements within the code diagram for…
If f maps a discrete d-manifold G onto a (k+1)-partite complex P then H(G,f,P),the set of simplices x in G such that f(x) contains at least one facet in P defines a (d-k)-manifold.
This note shows the compatibility of the differential geometric and the topological formulations of equivariant characteristic classes for a compact connected Lie group action.
Examples of nonformal simply connected symplectic manifolds are constructed.
A simplicial complex $\Delta$ is called flag if all minimal nonfaces of $\Delta$ have at most two elements. The following are proved: First, if $\Delta$ is a flag simplicial pseudomanifold of dimension $d-1$, then the graph of $\Delta$ (i)…
We show the existence of a convex compact domain in a quasi-Fuchsian manifold such that the induced metric on its boundary coincides with a prescribed surface metric of curvature $K\geq-1$ in the sense of A. D. Alexandrov.
We construct examples of (effective) closed orbifolds which are covered by manifolds, but not finitely so.
The shape and orientation of data clouds reflect variability in observations that can confound pattern recognition systems. Subspace methods, utilizing Grassmann manifolds, have been a great aid in dealing with such variability. However,…
Let G be a simple complex algebraic group. By using a notion of a G-category we define invariants of tangles with flat G-connections in their complements. We also show that quantized universal enveloping algebras at roots of unity provide…
Given a compact smooth manifold $M$ with non-empty boundary and a Morse function, a pseudo-gradient Morse-Smale vector field adapted to the boundary allows one to build a Morse complex whose homology is isomorphic to the (absolute or…
In this paper, we introduce the foundation of a fractal topological space constructed via a family of nested topological spaces endowed with subspace topologies, where the number of topological spaces involved in this family is related to…