A note on irreducible Heegaard diagrams

Cavicchioli, Alberto; Spaggiari, Fulvia

doi:https://doi.org/10.1155/IJMMS/2006/53135

International Journal of Mathematics and Mathematical Sciences

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Volume 2006 | Article ID 053135 | https://doi.org/10.1155/IJMMS/2006/53135

A note on irreducible Heegaard diagrams

Alberto Cavicchioli¹and Fulvia Spaggiari¹

Received19 Dec 2005

Revised26 Apr 2006

Accepted07 May 2006

Published06 Jul 2006

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.

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Copyright © 2006 Hindawi Publishing Corporation. 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.

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