$L^2$-Euler characteristics and the Thurston norm

Stefan Friedl; Wolfgang Lück

doi:10.1112/plms.12202

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arXiv · 1609.07805

$L^2$-Euler characteristics and the Thurston norm

Stefan Friedl·Wolfgang Lück

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Abstract

We assign to a finite $CW$-complex and an element in its first cohomology group a twisted version of the $L^2$-Euler characteristic and study its main properties. In the case of an irreducible orientable $3$-manifold with empty or toroidal boundary and infinite fundamental group we identify it with the Thurston norm. We will use the $L^2$-Euler characteristic to address the problem whether the existence of a map inducing an epimorphism on fundamental groups implies an inequality of the Thurston norms.

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BibTeX RIS

Stefan Friedl, Wolfgang Lück. 2016-09-25. $L^2$-Euler characteristics and the Thurston norm. https://doi.org/10.1112/plms.12202

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