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Leertaste = Abspielen/Pausieren

m = Stumm

f = Vollbild

Pfeil-links = Zurückspulen

Pfeil-rechts = Vorspulen

*Abstract:*

Let *W* be the exterior of a knot in a homology sphere and let *M* be an
amalgamation of *W* and any other compact 3-manifold along boundary
torus. Let *N* be the manifold obtained by pinching *W* into a solid
torus. This means that there is a degree-one map from *M* to *N*. We
prove that the Heegaard genus of *M* is at least as large as the
Heegaard genus of *N*. An immediate corollary is that the tunnel number
of a satellite knot is at least as large as the tunnel number of its
pattern knot.