On Differential Structure for Projective Limits of Manifolds
Mathematical Physics
2009-10-31 v2 High Energy Physics - Theory
Differential Geometry
math.MP
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.
Cite
@article{arxiv.math-ph/9804007,
title = {On Differential Structure for Projective Limits of Manifolds},
author = {M. C. Abbati and A. Mania'},
journal= {arXiv preprint arXiv:math-ph/9804007},
year = {2009}
}
Comments
38 pages, Latex 2e, to be published on J. Geom. Phys minor misprints corrected, reference added