Related papers: Spaces of geometrically generic configurations

Extending earlier work(*), we examine the deformation of the canonical symplectic structure in a cotangent bundle $T^\star(\Q)$ by additional terms implying the Poisson non-commutativity of both configuration and momentum variables. In this…

Let G = S^d, d = 0, 1 or 3, act freely on a finitistic connected space X. This paper gives the cohomology classification of X if a mod 2 or rational cohomology of the orbit space X/G is isomorphic to the product of a projective space and…

A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced…

Using spaces of homomorphisms and the descending central series of the free groups, simplicial spaces are constructed for each integer q>1 and every topological group G, with realizations B(q,G) that filter the classifying space BG. In…

Let M be a compact Kahler manifold equipped with a Hamiltonian action of a compact Lie group G. In this paper, we study the geometric quantization of the symplectic quotient M//G. Guillemin and Sternberg [Invent. Math. 67 (1982), 515--538]…

Paths in an appropriate geometry are usually used as trajectories of test particles in geometric theories of gravity. It is shown that non-symmetric geometries possess some interesting quantum features. Without carrying out any quantization…

A noncommutative *-algebra that generalizes the canonical commutation relations and that is covariant under the quantum groups SOq(3) or SOq(1,3) is introduced. The generating elements of this algebra are hermitean and can be identified…

Let $V$ be a projective subvariety of $\mathbb P^n(\mathbb C)$. A family of hypersurfaces $\{Q_i\}_{i=1}^q$ in $\mathbb P^n(\mathbb C)$ is said to be in $N$-subgeneral position with respect to $V$ if for any $1\le i_1<\cdots <i_{N+1}$, $…

We determine explicit formulas for geodesics (in the Euclidean metric) in the configuration space of ordered pairs (x,x') of points in R^n which satisfy d(x,x')>=epsilon. We interpret this as two or three (depending on the parity of n)…

A quantum graph $\mathcal{G}$ housed by a matrix algebra $M_n$ can be encoded as an operator system $\mathcal S=\mathcal{S}_{\mathcal{G}}\le M_n$. There are two sensible notions of quantum automorphism group for any such:…

This is a survey article of geometric properties of noncommutative symmetric spaces of measurable operators $E(\mathcal{M},\tau)$, where $\mathcal{M}$ is a semifinite von Neumann algebra with a faithful, normal, semifinite trace $\tau$, and…

This paper begins by extending the notion of a combinatorial configuration of points and lines to a combinatorial configuration of points and planes that we refer to as configurations of order $2$. We then proceed to investigate a further…

The complement of an arrangement A of a finite number of affine hyperplanes in complex n-space has the structure of a poset of spaces indexed by the intersection poset, L(A). The space corresponding to G in L(A) is homotopy equivalent to…

The general ideal of this paper is to answer the following question: given a numerical property of commuting graphs, a class of semigroups $\mathcal{C}$ and $n\in\mathbb{N}$, is it possible to find a semigroup in $\mathcal{C}$ such that the…

A special generic map is a smooth map regarded as a natural generalization of Morse functions with just 2 singular points on homotopy spheres. Canonical projections of unit spheres are simplest examples of such maps and manifolds admitting…

We consider the space $F_n$ of configurations of $n$ points in $P^2$ satisfying the condition that no three of the points lie on a line. For $n = 4, 5, 6$, we compute $H^*(F_n; \mathbb{Q})$ as an $S_n$-representation. The cases $n = 5, 6$…

Embedding of a Green-Schwarz superbrane into a generic curved target space in a general covariant way is considered. It is demonstrated explicitely, that the customary superbrane formulation based on finite-component spinors extends to a…

The configuration space $\mathcal{C}^n(X)$ of an algebraic curve $X$ is the algebraic variety consisting of all $n$-point subsets $Q\subset X$. We describe the automorphisms of $\mathcal{C}^n(\mathbb{C})$, deduce that the (infinite…

The topology of spaces of Hermitian operators in $C^n$ with non-simple spectra was studied by V.Arnold in a relation with the theory of adiabatic connections and the quantum Hall effect. The natural filtration of these spaces by the sets of…

It is proved some results about existence and non existence of unit normal sections of submanifolds of the Euclidean space and sphere which associated Gauss maps are harmonic. Some applications to CMC hypersurfaces of the sphere and…