I heard about manifolds with boundaries, but I never heard about manifolds with boundaries and vertices except perhaps in Spivak's book. Take a solid cube. It's a 3-dimensional manifold with a boundary and 8 vertices. So I think manifolds with boundaries and vertices are natural objects of mathematics. Particularly I'd like to see a proof of Stokes' theorem on these manifolds. Are there books which treat these manifolds?
Manifolds with boundaries and vertices
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manifolds
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0See this post on MO:http://mathoverflow.net/questions/12920/stokes-theorem-for-manifolds-with-corners – 2012-04-19
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0@Brett Thanks a lot. – 2012-04-20