A Hilbert reciprocity law on 3-manifolds

被引：1

作者：

Niibo, Hirofumi ^{[1
]}

Ueki, Jun ^{[2
]}

机构：

[1] Supership Inc, Toranomon Hills 27F,1-17-1 Toranomon,Minato Ku, Tokyo 1056427, Japan

[2] Ochanomizu Univ, Fac Sci, Dept Math, 2-1-1 Otsuka,Bunkyo Ku, Tokyo 1128610, Japan

来源：

RESEARCH IN THE MATHEMATICAL SCIENCES | 2023年 / 10卷 / 01期

关键词：

Knot; 3-manifold; Idelic class field theory; Hilbert symbol; Arithmetic topology; CLASS FIELD-THEORY;

D O I：

10.1007/s40687-022-00364-w

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Based on our homological idelic class field theory, we formulate an analogue of the Hilbert reciprocity law on a rational homology 3-sphere endowed with an infinite link, in the spirit of arithmetic topology; we regard the intersection form on the unitary normal bundle of each knot as an analogue of the Hilbert symbol at each prime ideal to formulate the Hilbert reciprocity law, ensuring that cyclic covers of links are analogues of Kummer extensions.

引用

页数：8

共 17 条

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