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Symplectic and Poisson geometry seminar: A diffeological approach to solving the integration problem

Event Type
347 Altgeld Hall
Apr 4, 2022   3:00 pm  
Joel Villatoro
Joey Palmer

In the theory of Lie groupoids and Lie algebroids, there is a procedure for differentiting a Lie groupoid to result in a Lie algebroid. This process is very much analogous to the construction of a Lie algebra from a Lie group. From this analogy, it is reasonable to ask whether or not it is possible to construct a Lie groupoid given the data of a Lie algebroid in much the same manner tha you do for Lie algebras. In fact, it turns out tha this is not possible due to the fact tha integration procedure results in something tha is not quite a manifold. In this talk I will discuss an approach to patching this problem using diffeological spaces which are a generalization of smooth manifolds.

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