Guts in Sutured Decompositions and the Thurston Norm

Ian Agol; Yue Zhang

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arXiv · 2203.12095

Guts in Sutured Decompositions and the Thurston Norm

Ian Agol·Yue Zhang

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Abstract

We construct an invariant called guts for second homology classes in irreducible 3-manifolds with toral boundary and non-degenerate 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, an invariant of knot complements is given and is computed in a few interesting cases. Besides, we show that the dimension of a maximal simplex in a Kakimizu Complex is an invariant.

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Ian Agol, Yue Zhang. 2022-03-22. Guts in Sutured Decompositions and the Thurston Norm. https://arxiv.org/abs/2203.12095

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