On the Iwasawa invariants of a link in the 3-sphere
Teruhisa Kadokami, Yasushi Mizusawa
TL;DR
This paper explores the Iwasawa invariants of links in the 3-sphere, drawing analogies with number theory, and investigates the existence of covers with specific invariants and related conjectures.
Contribution
It introduces the study of Iwasawa invariants for links in the 3-sphere and examines the existence of covers with prescribed invariants, extending number theory analogies.
Findings
Existence results for covers with given Iwasawa invariants
Proposed analogies to Greenberg's conjecture in link theory
Discussion of number-theoretic analogies in topology
Abstract
Based on the analogy between knots and primes, J. Hillman, D. Matei and M. Morishita defined the Iwasawa invariants for sequences of cyclic covers of links with an analogue of Iwasawa's class number formula of number fields. In this paper, we consider the existence of covers of links with prescribed Iwasawa invariants, discussing analogies in number theory. We also propose and consider a problem analogous to Greenberg's conjecture.
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Taxonomy
TopicsGeometric and Algebraic Topology · Algebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology