A \(C^*\)-algebra of geometric operators on self-similar CW-complexes. Novikov-Shubin and \(L^2\)-Betti numbers

DOI10.1016/j.jfa.2008.10.013zbMath1161.46043arXivmath/0607603OpenAlexW2018585279MaRDI QIDQ1000527

Tommaso Isola, Daniele Guido, Fabio Cipriano

Publication date: 9 February 2009

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0607603

zbMATH Keywords

combinatorial Laplacianfractal graphs\(L^2\)-invariantsself-similar CW-complexestraces on amenable spaces

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Relations of low-dimensional topology with graph theory (57M15) Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89) PL-topology (57Q99)

Related Items (2)

A spectral triple for a solenoid based on the Sierpinski gasket ⋮ A trace on fractal graphs and the Ihara zeta function

Cites Work

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• On the quasi-isometry invariance of \(L^ 2\)-Betti numbers
• \(L^{2}\)-spectral invariants and convergent sequences of finite graphs
• An index theorem on open manifolds. I. II
• Von Neumann spectra near zero
• De Rham-Hodge theory for \(L^2\)-cohomology of infinite coverings
• Approximating \(L^2\) invariants of amenable covering spaces: A combinatorial approach
• Estimates of transition densities for Brownian motion of nested fractals
• Dimensions and singular traces for spectral triples, with applications to fractals
• Noncommutative Riemann integration and Novikov-Shubin invariants for open manifolds
• \(L^ 2\)-topological invariants of 3-manifolds
• Harnack inequalities and sub-Gaussian estimates for random walks
• Which values of the volume growth and escape time exponent are possible for a graph?
• Combinatorial heat kernels and index theorems
• BOSE–EINSTEIN CONDENSATION ON INHOMOGENEOUS AMENABLE GRAPHS
• A trace on fractal graphs and the Ihara zeta function
• Effective resistances for harmonic structures on p.c.f. self-similar sets
• Aperiodic order and quasicrystals: spectral properties
• Self-similarity of volume measures for Laplacians on p. c. f. self-similar fractals

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