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3-manifold ambient isotopy assume bordism boundary component bundle c-disk cohomology commutative compact complex compressing disk conjugate consider contained Corollary corresponding Coxeter group Coxeter system curve cusp decomposition defined Definition Dehn Dehn twists denote diagram Dieudonné Dieudonné module disc disjoint edge group element essential finite flat/charged functor genus geodesic graph handlebody Heegaard splittings Heegaard surface Hence homeomorphic homology homotopy Hopf algebras hyperbolic incompressible incompressible surface induced inessential intersects invariant irreducible isomorphism knot label Lemma manifold Math matrix factorization module monodromy morphism non-compact obtained open book oriented polynomial presheaf proper ambient isotopy properly embedded Proposition punctured disk QHFT regular neighborhood relative Heegaard representations result Section sequence slide-moves smooth stacks space spine structure subgroup submanifold subset Suppose tensor Theorem 1.1 Thom class Thurston norm topological torus triangulation trivial twisted vector vertex group vertices virtual