Effective finiteness of irreducible Heegaard splittings of non-Haken 3-manifolds
Name
1411.2509.pdf
Description
Submitted version
Size
356.89 KB
Format
Adobe PDF
Checksum (MD5)
087d836c45ca0408b58a8af416190156
Author(s)
Colding, Tobias
Gabai, David
Date Issued
October 2018
Journal
Duke Mathematical Journal
Publisher
Duke University Press
Citation
Colding, Tobias Holck and David Gabai. "Effective finiteness of irreducible Heegaard splittings of non-Haken 3-manifolds. Duke Mathematical Journal 167, 15 (October 2018): 2793-2832 © 2018 Duke University Press
Version
Original manuscript
Abstract
The main result is a short effective proof of Tao Li's theorem that a closed non-Haken hyperbolic 3-manifolds. N has at most finitely many irreducible Heegaard splittings. Along the way we show that N has finitely many branched surfaces of pinched negative sectional curvature carrying all closed index-≤ 1 minimal surfaces. This effective result, together with the sequel with Daniel Ketover, solves the classification problem for Heegaard splittings of non-Haken hyperbolic 3-manifolds. Keywords: Heegaard splitting; 3-manifold; lamination; hyperbolic; minimal surface
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1215/00127094-2018-0022
