相关论文: On smoothness of isometries between orbit spaces
We study the moduli space of frozen planet orbits in the Helium atom for an interpolation between instantaneous and mean interactions and show that this moduli space is compact.
In this paper we study monomial multiple structures on a linear subspace of codimension two in projective space. We show that these structures determine smooth points in their respective Hilbert schemes, with (smooth) neighbourhoods of two…
The topology of the orbit space, $Y$, for the action of the complex conjugation on a complex surface, $X$, defined over reals, is studied. I give a criterion for blow-up stable triviality of $Y$ (which implies vanishing of its…
We introduce the notion of approximate smoothness in a normed linear space. We characterize this property and show the connections between smoothness and approximate smoothness for some spaces. As an application, we consider in particular…
We establish new results and introduce new methods in the theory of measurable orbit equivalence, using bounded cohomology of group representations. Our rigidity statements hold for a wide (uncountable) class of groups arising from negative…
A natural metric on the space of all almost hermitian structures on a given manifold is investigated.
We construct a metric on the moduli space of bodies in Euclidean space. The moduli space is defined as the quotient space with respect to the action of integral affine transformations. This moduli space contains a subspace, the moduli space…
We present a reduction of the Hilbert-Smith conjecture in the case of the finite dimensional orbit space to some algebraic topology problems.
A number of recent papers have studied when symmetry causes frameworks on a graph to become infinitesimally flexible, or stressed, and when it has no impact. A number of other recent papers have studied special classes of frameworks on…
We discuss selected topics on the topology of moduli spaces of curves and maps, emphasizing their relation with Gromov--Witten theory and integrable systems.
The problem in question is whether the quotient space of a compact linear group is a topological manifold and whether it is a homological manifold. In the paper, the case of an infinite group with commutative connected component is…
An 'isomorphism' between the 'moduli space' of star products on $\R^2$ and the 'moduli space' of all formal Poisson structures on $\R^2$ is established.
We give a survey of the theory of affine spheres, emphasizing the convex cases and relationsships to Monge-Ampere equations and geometric structures on manifolds.
We define a natural compactification of an arrangement complement in a ball quotient. We show that when this complement has a moduli space interpretation, then this compactification is often one that appears naturally by means of geometric…
Let $M$ be a compact smooth manifold with corners and $N$ be a finite dimensional smooth manifold without boundary which admits local addition. We define a smooth manifold structure to general sets of continuous mapings $\mathcal{F}(M,N)$…
We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under…
Given an orthogonal representation of a compact group, we show that any element of the connected component of the isometry group of the orbit space lifts to an equivariant isometry of the original Euclidean space. Corollaries include a…
We review a surprising correspondence between certain two-dimensional integrable models and the spectral theory of ordinary differential equations. Particular emphasis is given to the relevance of this correspondence to certain problems in…
This is a survey paper about a selection of results in complex algebraic geometry that appeared in the recent and less recent litterature, and in which rational homogeneous spaces play a prominent r{\^o}le. This selection is largely…
In this letter we briefly investigate the mathematical structure of space-time in the framework of discretization. It is shown that the discreteness of space-time may result in a new mechanical system which differ from the usual quantum…