Idèlic class field theory for 3-manifolds

2013/11/21 by Hirofumi Niibo, Niibo, Hirofumi · 2 citations
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.1311.5314

arxiv created 2013/12/11 · arxiv updated 2013/12/12

Abstract

Following the analogies between 3-dimensional topology and number theory, we study an idèlic form of class field theory for 3-manifolds. For a certain set K of knots in a 3-manifold M, we first present a local theory for each knot in K, which is analogous to local class field theory, and then, getteing together over all knots in K, we give an analogue of idèlic global class field theory for an integral homology sphere M.

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• Arithmetic invariants of torus links
• On genus theory for 3-manifolds in arithmetic topology

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