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Degree of $L^2$-Alexander torsion for 3-manifolds
Author:Xiaodong Pan   Nov 25, 2015     Hits:  

Speaker: Yi Liu  (BICM)


Time: Nov. 10, pm4:00---5:00, 2015


Room: X2511


Title:Degree of $L^2$-Alexander torsion for 3-manifolds


Abstract:For an irreducible orientable compact $3$-manifold $N$ with empty or incompressible toral boundary, the full $L^2$--Alexander torsion $\tau^{(2)}(N,\phi)(t)$ associated to any real first cohomology class $\phi$ of $N$ is represented by a function of a positive real variable $t$. In this talk, I will show that $\tau^{(2)}(N,\phi)$ is continuous, everywhere positive, and asymptotically monomial in both ends. Moreover, the degree of $\tau^{(2)}(N,\phi)$ equals the Thurston norm of $\phi$.

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