On the Euler class one conjecture for fillable contact structures

2024/09/22 by Liu, Yi · 2 citations
#57K18 #FOS: Mathematics #Geometric Topology (math.GT) #Primary 57K32 #Secondary 57K33

paper · doi:10.48550/arxiv.2409.14504

Abstract

In this paper, it is proved that every oriented closed hyperbolic 3--manifold N admits some finite cover M with the following property. There exists some even lattice point w on the boundary of the dual Thurston norm unit ball of M, such that w is not the real Euler class of any weakly symplectically fillable contact structure on M. In particular, w is not the real Euler class of any transversely oriented, taut foliation on M. This supplies new counter-examples to Thurston's Euler class one conjecture.

Cited by

• On 3-manifolds admitting co-orientable taut foliations, but none with vanishing Euler class
• Note on Euler class 0 taut foliation on the Whitehead link exterior

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