On the top-dimensional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>ℓ</mml:mi> <mml:mn>2</mml:mn> </mml:msup></mml:math>-Betti numbers
نویسندگان
چکیده
The purpose of this note is to introduce a trick which relates the (non)-vanishing top-dimensional $\ell^2$-Betti numbers actions with that sub-actions. We provide three different types applications: we prove Aut($F_n$) and Out($F_n$) (and their Torelli subgroups) do not vanish in degree equal virtual cohomological dimension, subgroups 3-manifold groups have vanishing 3 2 for instance $F_2^d \times Z$ has ergodic dimension $d + 1$.
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ژورنال
عنوان ژورنال: Annales de la Faculté des Sciences de Toulouse
سال: 2022
ISSN: ['0240-2963', '2258-7519']
DOI: https://doi.org/10.5802/afst.1695