m at h . A G ] 1 4 Ju l 1 99 9 L ∞ - algebra of an unobstructed deformation functor

6 J ul 1 99 9 L ∞ - algebra of an unobstructed deformation functor

ar X iv : m at h / 99 07 16 9 v 1 [ m at h . Q A ] 2 6 Ju l 1 99 9 Integrable deformations of Hamiltonian systems and q - symmetries 1

The complete integrability of the hyperbolic Gaudin Hamiltonian and other related integrable systems is shown to be easily derived by taking into account their sl(2, R) coalgebra symmetry. By using the properties induced by such a coalgebra structure, it can be proven that the introduction of any quantum deformation of the sl(2, R) algebra will provide an integrable deformation for such systems...

ar X iv : m at h / 99 07 19 2 v 1 [ m at h . G N ] 3 0 Ju l 1 99 9 ASYMPTOTIC TOPOLOGY

We establish some basic theorems in dimension theory and absolute extensor theory in the coarse category of metric spaces. Some of the statements in this category can be translated in general topology language by applying the Higson corona functor. The relation of problems and results of this ‘Asymptotic Topology’ to Novikov and similar conjectures is discussed.

ar X iv : m at h / 99 07 08 5 v 1 [ m at h . G R ] 1 3 Ju l 1 99 9 LOOPS AND SEMIDIRECT PRODUCTS

ar X iv : h ep - t h / 95 07 11 6 v 1 2 1 Ju l 1 99 5 A q - deformation of the Coulomb Problem

The algebra of observables of SOq(3)-symmetric quantum mechanics is extended to include the inverse 1 R of the radial coordinate and used to obtain eigenvalues and eigenfunctions of a q-deformed Coulomb Hamiltonian. Supported by an NSF fellowship; e-mail [email protected] Supported in part by NSF grant PHY-91-23780; e-mail [email protected]