Skip to content
DraconiticResearch
Search Sources API
203,948 studies31 sourcesUpdated 48 min ago
Peer-reviewedCC BYGeometry & Topology

Guts in sutured decompositions and the Thurston norm

  • Ian Agol1
  • Yue Zhang1
  1. 1Department of Mathematics, University of California, Berkeley, Berkeley, CA, United States
Open at sourcePDFDOICite

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.1. Introduction 3169 2. The Thurston norm and sutured decompositions 3172 3. Guts components as sutured manifolds 3176 4. Guts and Thurston cones 3186 5. Restriction map to the guts in homology 3189 6. Guts and sutured decomposition 3195 7. Examples of guts 3195 8. Guts and Kakimizu complex 3201 9. Conclusion

Related

  1. The Thurston spine and equivariant cell decompositions in genus 2
    Ni An, Jiexing Chen, Ingrid Irmer +1
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  2. Thurston norm, polytopes and splitting complexity
    Andrei Jaikin-Zapirain, Monika Kudlinska, Pablo Sánchez-Peralta
    arXivPreprintarXiv licenceFull textAlgebra & number theoryGeometry & topologyarXiv
  3. ℤp-folded surfaces and the ℤp-Thurston norm
    William Hobkirk
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  4. Wold-type decompositions for norm-increasing m-concave weighted shifts on directed trees
    Ashish Kujur
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  5. Norm-One Torus Decompositions and Decoding of Gashkov-Sidel'nikov Codes
    Minjia Shi, Shitao Li, Yuhong Xia +2
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@article{agol2026guts,
  title = {{Guts in sutured decompositions and the Thurston norm}},
  author = {Ian Agol and Yue Zhang},
  journal = {Geometry \& Topology},
  year = {2026},
  month = oct,
  doi = {10.2140/gt.2026.30.3169},
  url = {https://doi.org/10.2140/gt.2026.30.3169},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Guts in sutured decompositions and the Thurston norm
AU  - Ian Agol
AU  - Yue Zhang
PY  - 2026
DA  - 2026/10/12
JO  - Geometry & Topology
DO  - 10.2140/gt.2026.30.3169
UR  - https://doi.org/10.2140/gt.2026.30.3169
AB  - 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.1. Introduction 3169 2. The Thurston norm and sutured decompositions 3172 3. Guts components as sutured manifolds 3176 4. Guts and Thurston cones 3186 5. Restriction map to the guts in homology 3189 6. Guts and sutured decomposition 3195 7. Examples of guts 3195 8. Guts and Kakimizu complex 3201 9. Conclusion
SN  - 1364-0380
SN  - 1465-3060
ER  -