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On the Iwasawa invariants for links and Kida’s formula

Jun Ueki

Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1, Komaba, Meguro-ku, Tokyo 153-8914, Japan

https://doi.org/10.1142/S0129167X17500355Cited by:4 (Source: Crossref)

Abstract

Analogues of Iwasawa invariants in the context of 3-dimensional topology have been studied by M. Morishita and others. In this paper, following the dictionary of arithmetic topology, we formulate an analogue of Kida’s formula on $λ$ $λ$ -invariants in a $p$ $p$ -extension of $ℤ_{p}$ -fields for 3-manifolds. The proof is given in a parallel manner to Iwasawa’s second proof, with use of $p$ -adic representations of a finite group. In the course of our arguments, we introduce the notion of a branched $ℤ_{p}$ -cover as an inverse system of cyclic branched $p$ -covers of 3-manifolds, generalize the Iwasawa type formula, and compute the Tate cohomology of 2-cycles explicitly.

Keywords:

AMSC: 57M12, 57M25, 57M27, 57M60, 11R23

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