A. Asada, Regularized calculus: an application of zeta-regularization to infinite dimensional geometry and analysis, Int. J. Geom. Methods Mod. Phys, vol.1, issue.1, pp.107-157, 2004.

A. Asada, Regularized form of the sphere of a Hilbert space with the determinant bundle, Proceedings of the 9th international conference on differential geometry and its applications, pp.397-409, 2004.

A. Batubenge, P. Iglesias-zemmour, Y. Karshon, and J. Watts, A.; Diffeological, Frölicher, and differential spaces, 2014.

A. Batubenge and P. Ntumba, On the way to Frölicher Lie groups, Quaestionnes Math, vol.28, pp.73-93, 2009.

A. Batubenge and M. H. Tshilombo, Topologies on product and coproduct Frölicher spaces, Demonstratio Math, vol.47, pp.1012-1024, 2014.

M. Bauer, M. Bruveris, P. Harms, and P. Michor, Vanishing geodesic distance for the Riemannian metric with geodesic equation the KdV-equation, Ann. Global Anal. Geom, vol.41, issue.4, pp.461-472, 2012.

M. Bauer, M. Bruveris, P. Harms, and P. Michor, Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism, group, Ann. Global Anal. Geom, vol.44, issue.1, pp.5-21, 2013.

M. Bauer, M. Bruveris, and P. Michor, Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group, Ann. Global Anal. Geom, vol.II, pp.361-368, 2013.

J. Brylinski, Loop spaces, characteristic classes and geometric quantization, Reprint of the 1993 edition, Modern Birkhäuser Classics, 2008.

J. D. Christensen, G. Sinnamon, and E. Wu, The D-topology for diffeological spaces, Pacific Journal of Mathematics, vol.272, issue.1, pp.87-110, 2014.

P. Cherenack and P. Ntumba, Spaces with differentiable structure an application to cosmology, vol.34, pp.161-180, 2001.

D. Dugmore and P. Ntumba, On tangent cones of Frölicher spaces, Quaetiones mathematicae, vol.30, issue.1, pp.67-83, 2007.

D. Dugmore and P. Ntumba, Cofibrations in the category of Frölicher spaces: part I, Homotopy, homology and applications, vol.9, pp.413-444, 2007.

J. Eells, A setting for global analysis, Bull. Amer. Math. Soc, vol.72, pp.751-807, 1966.

H. Federer, Geometric measure theory, 1969.

D. Freed, The geometry of loop groups, J. Diff. Geom, vol.28, pp.223-276, 1988.

A. Frölicher and A. Kriegl, Linear spaces and differentiation theory Wiley series in Pure and Applied Mathematics, 1988.

H. Glöckner, Direct limits of infinite-dimensional Lie groups compared to direct limits in related categories, J. Funct. Anal, vol.245, pp.19-61, 2007.

P. Iglesias-zemmour and . Diffeology, Mathematical Surveys and Monographs, vol.185, 2013.

A. Kriegl and P. W. Michor, The convenient setting for global analysis, Math. surveys and monographs 53, 2000.

J. Leslie, On a Diffeological Group Realization of certain Generalized symmetrizable Kac-Moody Lie Algebras, J. Lie Theory, vol.13, pp.427-442, 2003.

J. Magnot, Difféologie du fibré d'Holonomie en dimension infinie, C. R. Math. Soc. Roy. Can, vol.28, issue.4, pp.121-128, 2006.

J. Magnot, Ambrose-Singer theorem on diffeological bundles and complete integrability of the KP equation, Int. J. Geom. Methods Mod. Phys, vol.10, issue.9, 2013.

P. Michor and D. Mumford, Riemannian geometries on spaces of plane curves, J. Eur. Math. Soc. (JEMS), vol.8, pp.1-48, 2006.

H. Omori, Infinite dimensional Lie groups, AMS translations of mathematical monographs, vol.158, 1997.

R. S. Palais, Homotopy theory of infinite dimensional manifolds, Topology, vol.5, pp.1-16, 1966.

A. Pressley and G. Segal, Loop Groups, 1988.

J. M. Souriau, Un algorithme générateur de structures quantiques, Astérisque, pp.341-399, 1985.

J. Watts, Diffeologies, differentiable spaces and symplectic geometry

T. Wurzbacher, Symplectic geometry of the loop space of a Riemannian manifold, Journal of Geometry and Physics, vol.16, pp.345-384, 1995.

. Larema, B. Angers, and . Lavoisier, F-49045 Angers cedex 01, and Lycée Jeanne d