Do classical constructions on differentiable manifolds like affine connections, Riemannian metrics, or (almost) complex structures have moduli spaces in category of diffeological spaces?
Does diffeology provide moduli for classical constructions?
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differential-geometry
1 Answers
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If you ask if the spaces of affine connections, riemannian metrics etc. are naturally diffeological spaces, the answer is yes. All these spaces are naturally equipped with the functional diffeology. They also can be equipped with the so-called compact controlled diffeology when the base manifold is non-compact, just to be sure that everything is going fine.