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The River Crossing Game David Goering and Dan Canada 3 The River Crossing Game is easy to describe: Each of two players distributes 11 boats (chips) at docks numbered from 2 to 12. More than one boat may be placed at a dock.
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We construct a pinching semiconjugacy from a quadratic polynomial $\fc(z)=z^2+c$ with $c \in (0, 1/4)$ to $\fq(z)=z^2+1/4$ on the sphere. By lifting this semiconjugacy to their natural extensions, we investigate the structure of the regular leaf space of $\fq$ in detail.
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