Hecke’s Theorem on the Different for 3-Manifolds

Hecke has shown that the different of an extension of number fields is a square in the ideal class group. We prove an analog for branched covers of closed <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>3</mml:mn> </mml:math> -manifolds saying that the branch divisor is a square in the first homology group.

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Publication Details

Journal
Annales de l’institut Fourier
Published
2026-01-26
DOI
https://doi.org/10.5802/aif.3751
Primary Topic
Geometric and Algebraic Topology
Type
article
Field-Weighted Citation Impact
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article

Hecke’s Theorem on the Different for 3-Manifolds

Will Sawin, Mark Shusterman
Annales de l’institut Fourier
Geometric and Algebraic Topology
article

Hecke’s Theorem on the Different for 3-Manifolds

Will Sawin, Mark Shusterman
article en

Abstract

Hecke has shown that the different of an extension of number fields is a square in the ideal class group. We prove an analog for branched covers of closed <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>3</mml:mn> </mml:math> -manifolds saying that the branch divisor is a square in the first homology group.

Annales de l’institut Fourier
Princeton University (US), Weizmann Institute of Science (IL)
Openalex Percentile: Top 72%
Geometric and Algebraic Topology
DOIOpen Access PDFOpenAlex
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Hecke’s Theorem on the Different for 3-Manifolds — Will Sawin, Mark Shusterman · Annales de l’institut Fourier (2026) | TGRS Research Map | TGRS