Concept

Cotangent space

Publications associées (11)

Hilbert Schemes as Moduli of Higgs Bundles and Local Systems

We construct five families of 2D moduli spaces of parabolic Higgs bundles (respectively, local systems) by taking the equivariant Hilbert scheme of a certain finite group acting on the cotangent bundle of an elliptic curve (respectively, twisted cotangent ...

Oxford University Press2014

Extensions of Lie-Rinehart algebras and cotangent bundle reduction

Tudor Ratiu

Let Q denote a smooth manifold acted upon smoothly by a Lie group G. The G-action lifts to an action on the total space TQ of the cotangent bundle of Q and hence on the standard symplectic Poisson algebra of smooth functions on TQ. The Poisson algebra of ...

Oxford University Press2013

The geometric structure of complex fluids

Tudor Ratiu, François Gay-Balmaz

This paper develops the theory of affine Euler-Poincare and affine Lie-Poisson reductions and applies these processes to various examples of complex fluids, including Yang-Mills and Hall magnetohydrodynamics for fluids and superfluids, spin glasses, microf ...

Elsevier2009

On Singular Poisson Sternberg Spaces

We obtain a theory of stratified Sternberg spaces thereby extending the theory of cotangent bundle reduction for free actions to the singular case where the action on the base manifold consists of only one orbit type. We find that the symplectic reduced sp ...

2009

Patrimoine, énergie, économie : conservation préventive et amélioration thermique des enveloppes de la Cité satellite du Lignon à Genève (1963-1971)

Franz Graf, Giulia Marino

Built between 1963 and 1971, the Lignon satellite precinct in Geneva (Georges Addor, Dominique Julliard, Louis Payot, Jacques Bolliger architects) is regarded as the most spectacular housing development in post-war Switzerland. The heritage protection agen ...

SCR/SKR2009

Affine Lie-Poisson reduction, Yang-Mills magnetohydrodynamics, and superfluids

Tudor Ratiu, François Gay-Balmaz

This paper develops the theory of affine Lie-Poisson reduction and applies this process to Yang-Mills and Hall magnetohydrodynamics for fluids and superfluids. As a consequence of this approach, the associated Poisson brackets are obtained by reduction of ...

2008

The symplectic normal space of a cotangent-lifted action

For the cotangent bundle T*Q of a smooth Riemannian manifold acted upon by the lift of a smooth and proper action by isometries of a Lie group, we characterize the symplectic normal space at any point. We show that this space splits as the direct sum of th ...

2008

Some applications of symmetries in differential geometry and dynamical systems

Oana Mihaela Dragulete

This thesis deals with applications of Lie symmetries in differential geometry and dynamical systems. The first chapter of the thesis studies the singular reduction of symmetries of cosphere bundles, the conservation properties of contact systems and their ...

EPFL2007

Tangent Vector Kernels for Invariant Image Classification with SVMs

Samy Bengio, Alexei Pozdnoukhov

This paper presents an application of the general sample-to-object approach to the problem of invariant image classification. The approach results in defining new SVM kernels based on tangent vectors that take into account prior information on known invari ...

2004

Topological defects and gravity in theories with extra dimensions

Ewald Rössl

Recent proposals of large and infinite extra dimensions triggered a strong research activity in theories in which our universe is considered as a sub-manifold of some higher-dimensional space-time, a so-called 3-brane. In this context, it is generally assu ...

EPFL2004

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