TY - JOUR
T1 - Effective finiteness of irreducible Heegaard splittings of non-Haken 3-manifolds
AU - Colding, Tobias Holck
AU - Gabai, David
N1 - Funding Information:
The first author was partially supported by National Science Foundation (NSF) grants DMS-11040934, DMS-1404540, and NSF Focused Research Group (FRG) grant DMS-0854774. The second author was partially supported by NSF grants DMS-1006553, DMS-1607374, and NSF FRG grant DMS-0854969.
Funding Information:
We thank Joseph Maher, Harold Rosenberg, and the referees for their constructive comments. The first author was partially supported by National Science Foundation (NSF) grants DMS-11040934, DMS-1404540, and NSF Focused Research Group (FRG) grant DMS-0854774. The second author was partially supported by NSF grants DMS-1006553, DMS-1607374, and NSF FRG grant DMS-0854969.
Publisher Copyright:
© 2018.
PY - 2018/10/1
Y1 - 2018/10/1
N2 - The main result is a short effective proof of Tao Li's theorem that a closed non-Haken hyperbolic 3-manifold 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.
AB - The main result is a short effective proof of Tao Li's theorem that a closed non-Haken hyperbolic 3-manifold 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.
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U2 - 10.1215/00127094-2018-0022
DO - 10.1215/00127094-2018-0022
M3 - Article
AN - SCOPUS:85055283344
SN - 0012-7094
VL - 167
SP - 2793
EP - 2832
JO - Duke Mathematical Journal
JF - Duke Mathematical Journal
IS - 15
ER -