Controlled Algebraic G-theory
نویسندگان
چکیده
This paper extends the notion of geometric control in algebraic K-theory from additive categories with split exact sequences to other exact structures. In particular, we construct exact categories of modules over a noetherian ring filtered by subsets of a metric space and sensitive to the large scale properties of the space. The algebraic K-theory of these categories is related to the controlled K-theory of geometric modules the way G-theory is classically related to K-theory. We recover familiar results in the new setting, including nonconnective controlled excision, equivariant properties, and prove the G-theoretic Novikov conjecture which is shown to be stronger than the usual K-theoretic conjecture.
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