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SUMMARY:The strong Atiyah conjecture for graph of groups via universal loc
 alizations. - Pablo Sánchez-Peralta\, UAM
DTSTART:20250228T134500Z
DTEND:20250228T144500Z
UID:TALK224419@talks.cam.ac.uk
CONTACT:Macarena Arenas
DESCRIPTION:The study of the rationality of the $L^2$-Betti numbers of a c
 ountable group has led to the development of a rich theory in $L^2$-homolo
 gy with deep implications in structural properties of the groups. For deca
 des almost nothing has been known about the general question of whether th
 e strong Atiyah conjecture passes to free products of groups or not. In th
 is talk\, we will confirm that the strong Atiyah conjecture is stable unde
 r the graph of groups construction provided that the edge groups are finit
 e. We will also discuss how universal localizations can be used to extend 
 the result for general edge groups.
LOCATION:MR13
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