On Differential Structure for Projective Limits of Manifolds

Abstract

We investigate the differential calculus defined by Ashtekar and Lewandowski on projective limits of manifolds by means of cylindrical smooth functions and compare it with the C^infty calculus proposed by Froehlicher and Kriegl in more general context. For products of connected manifolds, a Boman theorem is proved, showing the equivalence of the two calculi in this particular case. Several examples of projective limits of manifolds are discussed, arising in String Theory and in loop quantization of Gauge Theories.

arXiv comment38 pages, Latex 2e, to be published on J. Geom. Phys minor misprints corrected, reference added

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