Genera of Arborescent Links: 1986
American Mathematical Soc., 1986 - 130 pages
Genera of the arborescent links ; Given a non-split oriented arborescent (often called algebraic, not be confused with complex algebraic) link we give an effective algorithm to construct a [italic]C[infinity symbol exponent] transversely oriented codimension one foliation [script]F on [italic]S3 - [italic]N̊([italic]L) such that [script]F is transverse to [partial derivative/boundary/degree of a polynomial symbol][italic]N̊([italic]L), [script]F and [script]F[[conditional event/restriction/such that symbol][partial derivative/boundary/degree of a polynomial symbol][italic]N̊([italic]L) have no Reeb components and some Seifert surface [italic]S is a compact leaf.
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Expressions et termes fréquents
3-manifold 4.7 to decompose Alexander polynomial algebraic Apply Lemma 4.7 ball neighborhood boundary candidate surface candidate tree choice cohomology convex Corollary decomposition define t(v denote depth 0 tangles depth v odd disc decomposable Euler characteristic Euler class Example exists externally flat tangle fiber fibration fibre follows by induction gotten hence holds homology class homology of 3-manifolds incompressible surface induction hypothesis integral lattice intersects isotope Kinoshita Terasaka tangle lattice points maximal depth minimal genus surface Murasugi sum non-singular closed 1-forms norm octahedron oriented 3-manifold oriented arborescent links oriented link plumbing potentially pretzel knots pretzel link projection proof of Theorem properly embedded Reeb components Remark result follows s(vi Seifert circles Seifert surface simple closed curves singular Step stump surface in Figure surface of minimal sutured manifold obtained T-projection taut foliation Theorem 4.2 Thurston torus torus-disk transversely oriented tree diagram twisted band unit ball vector vertices X_(S