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A note on irreducible Heegaard diagrams. (English) Zbl 1181.57027

Summary: We construct a Heegaard diagram of genus three for the real projective 3-space, which has no waves and pairs of complementary handles. The first example was given by Im and Kim but our diagram has smaller complexity. Furthermore the proof presented here is quite different from that of the quoted authors, and permits also to obtain a simple alternative proof of their result. Examples of irreducible Heegaard diagrams of certain connected sums complete the paper.

MSC:

57N10 Topology of general \(3\)-manifolds (MSC2010)
57M12 Low-dimensional topology of special (e.g., branched) coverings
57M25 Knots and links in the \(3\)-sphere (MSC2010)
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References:

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