98-42 M.C.Abbati, A.Mania`

On Differential Structure for Projective Limits of Manifolds (179K, Latex 2e) Jan 30, 98

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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 ${\cal C}^\infty$ calculus proposed by Fr\"ohlicher 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.

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