Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/iii/paper-141/1/a/solution

Label the unbounded region and the three lobe regions in cyclic order, and label the central region . The Dehn presentation of a knot group Heegaard diagram is obtained by thickening the projection graph: take one alpha compressing curve for each of , one beta curve for each crossing, and place the basepoint in . Orient and order the crossing curves so that their cyclic region words are
This intersection data, together with , specifies the requested pointed Heegaard diagram up to the usual isotopies and handle slides.

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