Lifted Heegaard Surfaces and Virtually Haken Manifolds

2010/01/29 by Zhang, Yu
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1001.5306

Abstract

In this paper, we give infinitely many non-Haken hyperbolic genus three 3-manifolds each of which has a finite cover whose induced Heegaard surface from some genus three Heegaard surface of the base manifold is reducible but can be compressed into an incompressible surface. This result supplements [CG] and extends [MMZ].

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• Critical Heegaard Surfaces
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• Heegaard genera in congruence towers of hyperbolic 3-manifolds