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Resolutions for unit groups of orders

We present a general algorithm for constructing a free resolution for unit groups of orders in semisimple rational algebras. The approach is based on computing a contractible $G$-complex employing the theory of minimal classes of quadratic forms and Opgenorth's theory of dual cones. The information from the complex is then used together with Wall's perturbation lemma to obtain the resolution.

preprint2016arXivOpen access
Sebastian Schönnenbeck
math.KT
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Sebastian Schönnenbeck

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