L2-Invariants: Theory and Applications to Geometry and K-Theory

By W. Lück. 2002

696 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f96856bc737def182b7b762a233f8028c7911ed8

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Hyperlinearity, essentially free actions and L2-invariants. The sofic property (2004, background): “ Atiyah Conjecture holds, then it holds for the limit group as well. First of all, Proposition 6.1 and Lemma 6.4 immediately show that if ∆ is a positive self-adjoint operator, then lndet(∆2) ≥ 0. By [11] lndet(∆2) = 2lndet(∆). Hence, Theorem 5 follows. Now, let (Γn,Sn)n≥1 be marked soﬁc groups of m”
On Invariants of Hirzebruch and Cheeger{Gromov (2003, background): “Both [14] and [15] are excellent references for ideas related to the von Neumann trace and its applications in geometry and topology.”
On the growth of $L^2$-invariants for sequences of lattices in Lie groups (2012, background): “It is then natural to investigate a secondary invariant such as the L(2)-torsion ofX , see [82, 23].”
3-Manifold Groups (2012, neutral): “4) The L(2)-Betti numbers b (2) i (X,α), for a given space X and a homomorphism α : π1(X) → Γ, were introduced by Atiyah [At76]; we refer to [Lü02] for details of the definition.”
ENTROPY, DETERMINANTS, AND L 2 -TORSION (2012, methodology): “We remark that the Fuglede-Kadison determinant used in [49] is a modified one, excluding the point 0 in the integral of (2.”
Compact Group Automorphisms, Addition Formulas and Fuglede-Kadison Determinants (2010, methodology): “It has found wide application in the study of L(2)-invariants [48].”
The rank gradient from a combinatorial viewpoint (2007, methodology): “groups Lück approximation gives a fast proof for Proposition 11.”
Group cocycles and the ring of affiliated operators (2007, background): “For more details about the definition of the dimension function and its properties consult [31].”
Processes on Unimodular Random Networks (2006, background): “13 of Lück (2002) for these implications and more information.”