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0111 · Feb 201319922001200920172026
4 results for Iglesias-Zemmour

Study on Čech-de Rham obstruction in diffeological spaces.

problem Obstruction to Čech-de Rham map being an isomorphism in diffeological spaces.
method Higher topos theory, homotopy pullback diagrams, Čech-de Rham bicomplex, \infty-stack cohomology.
result New exact sequences in all higher degrees and conceptual proof of cohomology agreement.

Diffeological spaces are generalizations of smooth manifolds which include singular spaces and function spaces. For each diffeological space, Iglesias-Zemmour introduced a natural topology called the DD-topology. However, the DD-topology has not yet been studied seriously in the existing literature. In this paper, we…

2013-02-12abs ↗pdf ↗

Diffeological submanifolds are a new type of submanifold in manifold theory.

problem Defining and understanding different types of submanifolds in manifold theory.
method Introducing diffeological submanifolds and comparing them with other types of submanifolds.
result A diffeological submanifold can be included in a manifold without being an immersion.