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The spectral measure of certain elements of the complex group ring of a wreath product | | Warren Dicks
; Thomas Schick
; | | Date: |
20 Jul 2001 | | Journal: | Geometriae Dedicata, 93 (2002), 121-137 | | Subject: | Geometric Topology; Group Theory; K-Theory and Homology; Rings and Algebras; Spectral Theory | math.GT math.GR math.KT math.RA math.SP | | Affiliation: | UA Barcelona), Thomas Schick (Muenster | | Abstract: | We use elementary methods to compute the L2-dimension of the eigenspaces of the Markov operator on the lamplighter group and of generalizations of this operator on other groups. In particular, we give a transparent explanation of the spectral measure of the Markov operator on the lamplighter group found by Grigorchuk-Zuk. The latter result was used by Grigorchuk-Linnell-Schick-Zuk to produce a counterexample to a strong version of the Atiyah conjecture about the range of L2-Betti numbers. We use our results to construct manifolds with certain L2-Betti numbers (given as convergent infinite sums of rational numbers) which are not obviously rational, but we have been unable to determine whether any of them are irrational. | | Source: | arXiv, math.GT/0107145 | | Services: | Forum | Review | PDF | Favorites | |
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