Cobordism groups of dihedral branched covers

Abstract

For every integer $n \geq 1$, we compute the cobordism groups of dihedral $n$-fold branched covers of $S^3$ with oriented and non-oriented branching sets. We show that the groups are cyclic, generated by the $n$-fold connected dihedral covers of $(2,n)$-torus links. The isomorphism types of the groups are detected using explicit cobordism invariants defined in terms of the Seifert forms on the branching sets, generalizing Cappell-Shaneson characteristic knots associated to dihedral covers.

Disclosure

“) = κ3 ([f ]) ± 2. Iterating this operation as needed, we arrive at a 3-fold irregular dihedral cover Y → S 3 which represents the trivial element of CobD3 (S 3 ). Note on the use of AI In the course of preparing this manuscript, we used Claude and ChatGpt to verify proofs and improve the exposition. AI proposed stating a single result, Theorem A, which covers both the oriented and non-orientable case. In a previous draft, those were treated separately.”

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Classification

Proof ideas or individual proof-step assistance

Multiplier

8

Verified

2026-08-23T05:00:31.167175Z

Structural counts