Geometry & Topology Monographs 12 (2007) 319–334

DOI: 10.2140/gtm.2007.12.319

arXiv: math.GT/0510386

Abstract

We construct a sequence of pairs of 3–manifolds (M₁ⁿ, M₂ⁿ) each with incompressible torus boundary and with the following two properties:

(1) For Mⁿ the result of a carefully chosen glueing of M₁ⁿ and M₂ⁿ along their boundary tori, the genera (g₁ⁿ, g₂ⁿ) of (M₁ⁿ, M₂ⁿ) and the genus gⁿ of Mⁿ satisfy the inequality
gⁿ/(g₁ⁿ + g₂ⁿ) < 1/2.

(2) The result of amalgamating certain unstabilized Heegaard splittings of M₁ⁿ and M₂ⁿ to form a Heegaard splitting of M produces a stabilized Heegaard splitting that can be destabilized successively n times.

Keywords

Heegaard genus, 3–manifolds, destabilizations

Mathematical Subject Classification

Primary: 57M27

References

Publication

Received: 20 January 2007
Revised: 12 March 2007
Accepted: 12 March 2007
Published: 3 December 2007

Authors