Volume 12 (2007)

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Degeneration of Heegaard genus, a survey

David Bachman and Ryan Derby-Talbot

Geometry & Topology Monographs 12 (2007) 1–15

DOI: 10.2140/gtm.2007.12.1

arXiv: math.GT/0606383

Abstract

We survey known (and unknown) results about the behavior of Heegaard genus of 3-manifolds constructed via various gluings. The constructions we consider are (1) gluing together two 3-manifolds with incompressible boundary, (2) gluing together the boundary components of surface×I, and (3) gluing a handlebody to the boundary of a 3-manifold. We detail those cases in which it is known when the Heegaard genus is less than what is expected after gluing.

Keywords

Heegaard splitting, incompressible surface

Mathematical Subject Classification

Primary: 57M99, 57N10

Secondary: 57M27

References
Publication

Received: 15 June 2006
Revised: 31 January 2007
Accepted: 8 February 2007
Published: 3 December 2007

Authors
David Bachman
Mathematics Department
Pitzer College
Claremont, CA 91711
USA
Ryan Derby-Talbot
Department of Mathematics
The American University in Cairo
113 Kasr El Aini St
PO Box 2511
Cairo 11511
Egypt