It is well-known that the Heegaard genus is additive under connected sum of 3-manifolds. We show that the Heegaard genus of contact 3-manifolds is not necessarily additive under contact connected sum. We also prove some basic properties of the contact genus (a.k.a. open book genus [Rubinstein J.H., Comparing open book and Heegaard decompositions of 3-manifolds, Turkish J. Math., 2003, 27(1), 189–196]) of 3-manifolds, and compute this invariant for some 3-manifolds.
@article{bwmeta1.element.doi-10_2478_s11533-011-0038-7,
author = {Burak Ozbagci},
title = {On the Heegaard genus of contact 3-manifolds},
journal = {Open Mathematics},
volume = {9},
year = {2011},
pages = {752-756},
zbl = {1233.57015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0038-7}
}
Burak Ozbagci. On the Heegaard genus of contact 3-manifolds. Open Mathematics, Tome 9 (2011) pp. 752-756. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0038-7/
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