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Five proofs that the Euler characteristic of a closed orientable surface is even
Let be a closed orientable surface of genus . (Below we will occasionally write , omitting the genus.) Then its Euler characteristic is even. In this post we will give five proofs of this fact that do...
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The Picard groups
Let be a commutative ring. From we can construct the category of -modules, which becomes a symmetric monoidal category when equipped with the tensor product of -modules. Now, whenever we have a...
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