A known general program, designed to endow the quotient space U / B of unitary groups , C ∗ algebras ⊂ with an invariant Finsler metric, is applied obtain a metric for I ( H ) partial isometries Hilbert . group × where algebra bounded linear operators in Under this solution best approximation problem leads computation minimal geodesics space. We find solutions problem, and study properties obta...

In this paper, we introduce the concepts of right, left and product stabilizers on hoops and study some properties and the relation between them.  And we try to find that how they can be equal and investigate that under what condition they can be filter, implicative filter, fantastic and positive implicative filter. Also, we prove that  right and product stabilizers are filters and if they are ...

We elaborate the formulation of $\mathsf{CP^{n-1}}$ sigma model with fermions as a gauged Gross-Neveu model. This approach allows to identify super phase space supersymplectic quotient. Potential chiral gauge anomalies are shown receive contributions from bosons and alike related properties this space. Along way we demonstrate that worldsheet supersymmetric is quotient target supersymmetry. Pos...

The main result of this paper is Theorem 2.13 which says that the quotient μ({1})/U associated to a quasi-hamiltonian space (M,ω, μ : M → U) has a symplectic structure even when 1 is not a regular value of the momentum map μ. Namely, it is a disjoint union of symplectic manifolds of possibly different dimensions, which generalizes the result of Alekseev, Malkin and Meinrenken in [AMM98]. We ill...

In this paper, we describe an example of a hyperkähler quotient of a Banach manifold by a Banach Lie group. Although the initial manifold is not diffeomorphic to a Hilbert manifold (not even to a manifold modelled on a reflexive Banach space), the quotient space obtained is a Hilbert manifold, which can be furthermore identified either with the cotangent space of a connected component Gr res, (...

In 1969, P. Deligne and D. Mumford compactified the moduli space of curves Mg,n. Their compactification Mg,n is a projective algebraic variety, and as such, it has an underlying analytic structure. Alternatively, the quotient of the augmented Teichmüller space by the action of the mapping class group gives a compactification of Mg,n. We put an analytic structure on this quotient and prove that ...

In this paper, we describe an example of a hyperkähler quotient of a Banach manifold by a Banach Lie group. Although the initial manifold is not diffeomorphic to a Hilbert manifold (not even to a manifold modelled on a reflexive Banach space), the quotient space obtained is a Hilbert manifold, which can furthermore be identified either with the cotangent space of a connected component Gr res of...

To determine what spaces are the images of “nice” spaces under “nice” mappings is one of the central questions of general topology in 1 . In the past, many noteworthy results on images of metric spaces have been obtained. For a survey in this field, see 2 , for example. A characterization for a quotient compact image of a locally separable metric space is obtained in 3 . Also, such a quotient i...