• Corpus ID: 5115113


  title={LUCK ’ S THEOREM},
  author={Alex Wright},
lim m→∞ bp(Xm) [Γ : Γm] exists, where bp(Xm) = dimH (Xm,C). In fact the limit is the much studied p-th L-Betti number of X. Luck’s Theorem answered a question of Gromov. That the limsup is at most the L-Betti number was previously established by Kazhdan. In this note we will try to see in an elementary way why this limit exists. The reader should look elsewhere for more general and powerful statements, as well as for context and applications. The author consulted the following sources while…