Torus decomposition and foliation detected slopes
Qingfeng Lyu

TL;DR
This paper proves that if a closed 3-manifold formed by gluing two knot manifolds admits a co-oriented taut foliation, then the gluing map aligns certain boundary slopes detected by the foliation, confirming a conjecture.
Contribution
It establishes a link between taut foliations and boundary slopes in glued knot manifolds, confirming a conjecture by Boyer, Gordon, and Hu.
Findings
If the manifold admits a taut foliation, the gluing map matches CTF-detected slopes.
The result confirms the conjecture relating foliation detection and boundary slopes.
Provides new insights into the structure of 3-manifolds with taut foliations.
Abstract
Let and be knot manifolds and be the closed 3-manifold obtained by gluing up and via . We show that if admits a co-oriented taut foliation, then identifies some CTF-detected rational boundary slopes of and , affirming a conjecture proposed by Boyer, Gordon and Hu.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics
