Approximation of $L_2$-torsion. · Question 1.1

Workshop introduction

This problem list concerns the study of the asymptotic behavior of some natural invariants of finitely generated groups.

Question context

Let $M$ be a closed Riemannian manifold and let $\Gamma=\pi_1(M)>\Gamma_1>\Gamma_2>\ldots$ be a decreasing sequence of finite index normal subgroups of $\Gamma$ with $\bigcap\Gamma_n=1$. Let $\tilde{M}$ be the universal cover of $M$ and let $M_n=\tilde{M}/\Gamma_n$.

In addition, suppose that $M$ is aspherical with $\dim M=2k+1$ and $\beta_j^{(2)}=0$ for every $j$.

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