Year: 2026
Type: article
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
Source: Geometry & Topology
Institution: University of California, Berkeley
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4221150403