International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 53135, 11 pages

A note on irreducible Heegaard diagrams

Alberto Cavicchioli and Fulvia Spaggiari

Dipartimento di Matematica, Università di Modena e Reggio Emilia, Via Campi 213/B, Modena 41100, Italy

Received 19 December 2005; Revised 26 April 2006; Accepted 7 May 2006

Copyright © 2006 Alberto Cavicchioli and Fulvia Spaggiari. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 to 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.