On the Heegaard genus of contact 3-manifolds
Burak Ozbagci
TL;DR
This paper investigates the behavior of the contact Heegaard genus in contact 3-manifolds, showing it is not always additive under contact connected sum and exploring its properties and computations.
Contribution
It demonstrates that contact Heegaard genus is not necessarily additive and provides foundational properties and computations of the contact genus.
Findings
Contact Heegaard genus is not additive under contact connected sum.
Basic properties of contact genus are established.
Computed contact genus for specific 3-manifolds.
Abstract
It is well-known that Heegaard genus is additive under connected sum of 3-manifolds. We show that 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) of 3-manifolds, and compute this invariant for some 3-manifolds.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Operator Algebra Research · Homotopy and Cohomology in Algebraic Topology