Sutured manifolds and $L^2$-Betti numbers

Gerrit Herrmann

Sutured manifolds and $L^2$-Betti numbers

Geometric Topology 2020-02-18 v2

Authors: Gerrit Herrmann

Abstract

Using the virtual fibering theorem of Agol we show that a sutured 3-manifold $(M, R_+,R_-,\gamma)$ is taut if and only if the $\ell^2$ -Betti numbers of the pair $(M,R_-)$ are zero. As an application we can characterize Thurston norm minimizing surfaces in a 3-manifold $N$ with empty or toroidal boundary by the vanishing of certain $\ell^2$ -Betti numbers.

Keywords

sutured manifolds l2-betti numbers virtual fibering theorem taut thurston norm 3-manifolds

Cite

@article{arxiv.1804.09519,
  title  = {Sutured manifolds and $L^2$-Betti numbers},
  author = {Gerrit Herrmann},
  journal= {arXiv preprint arXiv:1804.09519},
  year   = {2020}
}

Comments

In this version is a new application of the main theorem

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