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Algebraic Geometry over an Arbitrary Field Let A be an aﬃne k-algebra. This, in turn, continues to feed back into low-dimensional topology by providing a range of new invariants stemming from diagrammatic algebras. The book is very conceptual and also rigorous. All that remains in order to prove that is an abelian group is to show that + is an associative operation. The field emerged as a distinct area in the late 1980s and has many interactions with other parts of mathematics, including computational group theory, low-dimensional topology, algebraic topology, hyperbolic geometry, the study of Lie groups and their discrete subgroups and K-theory.

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