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Displaying similar documents to “Wedge cancellation and genus.”

On the Heegaard genus of contact 3-manifolds

Burak Ozbagci (2011)

Open Mathematics

Similarity:

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.

Heegaard and regular genus of 3-manifolds with boundary.

P. Cristofori, C. Gagliardi, L. Grasselli (1995)

Revista Matemática de la Universidad Complutense de Madrid

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By means of branched coverings techniques, we prove that the Heegaard genus and the regular genus of an orientable 3-manifold with boundary coincide.

Descent via (3,3)-isogeny on Jacobians of genus 2 curves

Nils Bruin, E. Victor Flynn, Damiano Testa (2014)

Acta Arithmetica

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We give a parametrization of curves C of genus 2 with a maximal isotropic (ℤ/3)² in J[3], where J is the Jacobian variety of C, and develop the theory required to perform descent via (3,3)-isogeny. We apply this to several examples, where it is shown that non-reducible Jacobians have non-trivial 3-part of the Tate-Shafarevich group.