International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 53135, 11 pages
doi:10.1155/IJMMS/2006/53135
A note on irreducible Heegaard diagrams
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.
Abstract
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.