Geodesic
Irrational $l^2$ invariants arising from the lamplighter group
Łukasz Grabowski1
1Lancaster University, UK
Groups, geometry, and dynamics, Tome 10 (2016) no. 2, pp. 795-817

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DOI

We show that the Novikov–Shubin invariant of an element of the integral group ring of the lamplighter group Z2​≀Z can be irrational. This disproves a conjecture of Lott and Lück. Furthermore we show that every positive real number is equal to the Novikov–Shubin invariant of some element of the real group ring of Z2​≀Z. Finally we show that the l2-Betti number of a matrix over the integral group ring of the group Zp​≀Z, where p is a natural number greater than 1, can be irrational. As such the groups Zp​≀Z become the simplest known examples which give rise to irrational l2-Betti numbers.
DOI : 10.4171/ggd/366
Classification : 20-XX, 57-XX
Mots-clés : l2-invariants, Atiyah conjecture, Novikov–Shubin invariants, l2-Betti numbers

Łukasz Grabowski  1

1 Lancaster University, UK 
Łukasz Grabowski. Irrational $l^2$ invariants arising from the lamplighter group. Groups, geometry, and dynamics, Tome 10 (2016) no. 2, pp. 795-817. doi: 10.4171/ggd/366
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     title = {Irrational $l^2$ invariants arising from the lamplighter group},
     journal = {Groups, geometry, and dynamics},
     pages = {795--817},
     year = {2016},
     volume = {10},
     number = {2},
     doi = {10.4171/ggd/366},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/366/}
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