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3-manifold spines and bijoins.

Luigi Grasselli (1990)

Revista Matemática de la Universidad Complutense de Madrid

We describe a combinatorial algorithm for constructing all orientable 3-manifolds with a given standard bidimensional spine by making use of the idea of bijoin (Bandieri and Gagliardi (1982), Graselli (1985)) over a suitable pseudosimplicial triangulation of the spine.

θ -curves inducing two different knots with the same 2 -fold branched covering spaces

Soo Hwan Kim, Yangkok Kim (2003)

Bollettino dell'Unione Matematica Italiana

For a knot K with a strong inversion i induced by an unknotting tunnel, we have a double covering projection Π : S 3 S 3 / i branched over a trivial knot Π fix i , where fix i is the axis of i . Then a set Π fix i K is called a θ -curve. We construct θ -curves and the Z 2 Z 2 cyclic branched coverings over θ -curves, having two non-isotopic Heegaard decompositions which are one stable equivalent.

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