M.C.Abbati, A.Mania`
On Differential Structure for Projective Limits of Manifolds
(179K, Latex 2e)
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.