25 citations · 82 across the 18 of their papers we have counts for
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An Example of Banach and Hilbert manifold: the universal Teichmüller space
Alice Barbara Tumpach
For , the group of Sobolev class s diffeomorphisms of the circle is a smooth manifold modeled on the space of Sobolev class s sections of the tangent bundle of the…
Banach Poisson-Lie groups and Bruhat-Poisson structure of the restricted Grassmannian
Alice Barbara Tumpach
The first part of this paper is devoted to the theory of Poisson-Lie groups in the Banach setting. Our starting point is the straightforward adaptation of the notion of Manin tripl…
Classification of infinite-dimensional irreducible Hermitian-symmetric affine coadjoint orbits
Alice Barbara Tumpach
In the finite-dimensional setting, every Hermitian-symmetric space of compact type is a coadjoint orbit of a finite-dimensional Lie group. It is natural to ask whether every infini…
Mostow's Decomposition Theorem for L*-groups and Applications to affine coadjoint orbits and stable manifolds
A. B. Tumpach
Mostow's Decomposition Theorem is a refinement of the polar decomposition. It states the following. Let G be a compact connected semi-simple Lie group with Lie algebra g. Given a s…
Infinite-dimensional hyperkaehler manifolds associated with Hermitian-symmetric affine coadjoint orbits
Alice Barbara Tumpach
This paper is devoted to the construction of a hyperkaehler structure on the complexification of any Hermitian-symmetric affine coadjoint orbit O of a semi-simple L*-group of compa…
Hyperkaehler structures and infinite-dimensional Grassmannians
A. B. Tumpach
In this paper, we describe an example of a hyperkaehler quotient of a Banach manifold by a Banach Lie group. Although the initial manifold is not diffeomorphic to a Hilbert manifol…