Open Access
Translator Disclaimer
2010 Topological Index Theory for surfaces in 3–manifolds
David Bachman
Geom. Topol. 14(1): 585-609 (2010). DOI: 10.2140/gt.2010.14.585


The disk complex of a surface in a 3–manifold is used to define its topological index. Surfaces with well-defined topological index are shown to generalize well known classes, such as incompressible, strongly irreducible and critical surfaces. The main result is that one may always isotope a surface H with topological index n to meet an incompressible surface F so that the sum of the indices of the components of HN(F) is at most n. This theorem and its corollaries generalize many known results about surfaces in 3–manifolds, and often provides more efficient proofs. The paper concludes with a list of questions and conjectures, including a natural generalization of Hempel’s distance to surfaces with topological index 2.


Download Citation

David Bachman. "Topological Index Theory for surfaces in 3–manifolds." Geom. Topol. 14 (1) 585 - 609, 2010.


Received: 12 January 2009; Revised: 19 November 2009; Accepted: 9 November 2009; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1206.57020
MathSciNet: MR2602846
Digital Object Identifier: 10.2140/gt.2010.14.585

Primary: 57M99

Keywords: Heegaard splitting , minimal surface

Rights: Copyright © 2010 Mathematical Sciences Publishers


Vol.14 • No. 1 • 2010
Back to Top