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Dec 21, 2015 at 9:12 answer added Nicola Ciccoli timeline score: 2
Dec 20, 2015 at 21:51 comment added user21574 you can construct it in the sense of distribution
Dec 20, 2015 at 16:16 comment added Qfwfq (continued) They have a notion of tangent bundle with which, I think, you can define a Poisson structure without problems. In the article Joyce says that his theory of manifolds-with-corners is tailored for applications to symplectic geometry.
Dec 20, 2015 at 16:09 comment added Qfwfq I think the objects you are considering (if a classical tetrahedron has to be among them), rather than "singular" smooth manifolds, are manifolds-with-corners in the sense of arxiv.org/abs/0910.3518
Dec 20, 2015 at 15:37 answer added Igor Khavkine timeline score: 6
Dec 20, 2015 at 7:35 history asked user60504 CC BY-SA 3.0