Guts in sutured decompositions and the Thurston norm

Agol, Ian; Zhang, Yue

doi:10.2140/gt.2026.30.3169

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ISSN (electronic): 1364-0380

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Guts in sutured decompositions and the Thurston norm

Ian Agol and Yue Zhang

Geometry & Topology 30 (2026) 3169–3205

DOI: 10.2140/gt.2026.30.3169

Abstract

We construct a sutured submanifold that is invariant up to isotopy, called guts, for second homology classes in irreducible 3-manifolds with toral boundary and nondegenerate Thurston norm. We prove that the guts of second homology classes in each Thurston cone are invariant under a natural condition. We show that the guts of different homology classes are related by sutured decompositions. As an application, a sutured submanifold of knot complements, that is invariant up to isotopy, is given and is computed in a few interesting cases. In addition, we show that the dimension of a maximal simplex in a Kakimizu complex is an invariant.

Keywords

3-manifold, Thurston norm, sutured manifold

Mathematical Subject Classification

Primary: 57K30, 57K31

References

Publication

Received: 28 March 2022

Revised: 17 April 2026

Accepted: 28 May 2026

Published: 12 October 2026

Proposed: David Gabai

Seconded: Jianfeng Lin, Mladen Bestvina

Authors

Ian Agol
Department of Mathematics University of California, Berkeley Berkeley, CA United States

Yue Zhang
Department of Mathematics University of California, Berkeley Berkeley, CA United States

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Volume 30, issue 9 (2026)