Extending fibrations of knot complements to ribbon disk complements

We show that stable commutator length is rational on free products of free abelian groups amalgamated over ℤk, a class of groups containing the fundamental groups of all torus knot complements. We consider a geometric model for these groups and parametrize all surfaces with specified boundary mapping to this space. Using this work we provide a topological algorithm to compute stable commutator length in these groups. Further, we use the methods developed to show that in free products of cyclic groups the stable commutator length of a fixed word varies quasirationally in the orders of the free factors.

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Closed incompressible surfaces in knot complements

Transactions of the American Mathematical Society ◽

10.1090/s0002-9947-99-02233-3 ◽

1999 ◽

Vol 352 (2) ◽

pp. 655-677 ◽

Cited By ~ 3

Author(s):

Elizabeth Finkelstein ◽

Yoav Moriah

Keyword(s):

Incompressible Surfaces ◽

Knot Complements

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Rigidity among prime-knot complements

Bulletin of the American Mathematical Society ◽

10.1090/s0273-0979-1986-15448-0 ◽

1986 ◽

Vol 14 (2) ◽

pp. 299-301 ◽

Cited By ~ 1

Author(s):

Wilbur Whitten

Keyword(s):

Knot Complements

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SEIFERT SURFACES IN KNOT COMPLEMENTS

Journal of Knot Theory and Its Ramifications ◽

10.1142/s0218216507005622 ◽

2007 ◽

Vol 16 (08) ◽

pp. 1053-1066 ◽

Cited By ~ 1

Author(s):

ENSIL KANG

Keyword(s):

Compact Surface ◽

Seifert Surface ◽

Normal Surface ◽

Incompressible Surface ◽

Ideal Triangulation ◽

Seifert Surfaces ◽

Knot Complements

In the ordinary normal surface for a compact 3-manifold, any incompressible, ∂-incompressible, compact surface can be moved by an isotopy to a normal surface [9]. But in a non-compact 3-manifold with an ideal triangulation, the existence of a normal surface representing an incompressible surface cannot be guaranteed. The figure-8 knot complement is presented in a counterexample in [12]. In this paper, we show the existence of normal Seifert surface under some restriction for a given ideal triangulation of the knot complement.

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