Analogies between Group Actions on 3-manifolds and Number Fields
نویسنده
چکیده
Let a cyclic group G act either on a number field L or on a 3-manifold M. Let sL be the number of ramified primes in the extension L ⊂ L and sM be the number of components of the branching set of the branched covering M → M/G. In this paper, we prove several formulas relating sL and sM to the induced G-action on Cl(L) and H1(M), respectively. We observe that the formulas for 3-manifolds and number fields are almost identical, and therefore, they provide new evidence for the correspondence between 3-manifolds and number fields postulated in arithmetic topology. This is an extended version of a paper which will appear in Comm. Math. Helv.
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