Cyclic Branched Coverings Over Some Classes of (1,1)-Knots

<table>A Heegaard diagram of <svg height="16.5625" id="M298" style="vertical-align:-3.50804pt" version="1.1" viewbox="0 0 81.212502 16.5625" width="81.212502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg> with a reducible 1-handle and its representation into a cylinder (<svg height="12.1125" id="M299" style="vertical-align:-3.50804pt" version="1.1" viewbox="0 0 8.4750004 12.1125" width="8.4750004" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M474 429q-19 -69 -47 -222l-65 -347q-8 -49 0 -60t49 -16l26 -3l-4 -26l-246 -12l4 25l17 3q37 6 50 20.5t23 60.5l67 321h-2q-65 -79 -150 -138q-69 -47 -104 -47q-28 0 -48.5 32t-20.5 81q0 78 35 148t90 117q67 57 161 77q23 5 58 5q43 0 90 -15zM387 387
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</svg> odd).</table>

Geometry

Cyclic Branched Coverings Over Some Classes of (1,1)-Knots

Figure 3