Cheeger constants and L2-Betti numbers
نویسندگان
چکیده
منابع مشابه
Integrality of L2-Betti numbers
The Atiyah conjecture predicts that the L-Betti numbers of a finite CW -complex with torsion-free fundamental group are integers. We establish the Atiyah conjecture, under the condition that it holds for G and that H G is a normal subgroup, for amalgamated free products G ∗H (H ⋊ F ). Here F is a free group and H ⋊ F is an arbitrary semi-direct product. This includes free products G∗F and semi-...
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The Platonic graphs πn arise in several contexts, most simply as a quotient of certain Cayley graphs associated to the projective special linear groups. We show that when n = p is prime, πn can be viewed as a complete multigraph in which each vertex is itself a wheel on n + 1 vertices. We prove a similar structure theorem for the case of an arbitrary prime power. These theorems are then used to...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2015
ISSN: 0012-7094
DOI: 10.1215/00127094-2871415