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Orbifold Spectral Theory
In this paper we study Sobolev spaces for smooth closed orientable Riemannian orbifolds. In particular we prove the Sobolev embedding theorem, the RellichKondrakov theorem and Poincare’sExpand
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$K$-theoretical index theorems for good orbifolds
In this note we study index theory for general and good orbifolds. We prove a A'-theoretical index theorem for good orbifolds, and from this we deduce as a corollary a numerical index formula. Let DExpand
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Wavelets and spectral triples for fractal representations of Cuntz algebras
In this article we provide an identification between the wavelet decompositions of certain fractal representations of $C^*-$algebras of directed graphs of M. Marcolli and A. Paolucci, and theExpand
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Purely atomic representations of higher-rank graph C*-algebras
We study purely atomic representations of C*-algebras associated to row-finite and source-free higher-rank graphs. We describe when purely atomic representations are unitarily equivalent and we giveExpand
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Equivariant spin bordism in low dimensions
Abstract We study Ω Spin, Z p n , n =5, 6, 7, where p is an odd prime and we consider some applications to the existence of Z p -invariant metrics of positive scalar curvature on closed spinExpand
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Symmetrized non-commutative tori
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Soft Non-commutative ToralC*-Algebras
We define parametrized softC*-algebras associated with finitely generated discrete groups and study in detail the ones associated to Zn. We determine theK-theory of the resultingC*-algebras for largeExpand
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Spectral triples and wavelets for higher-rank graphs
In this paper, we present a new way to associate a finitely summable spectral triple to a higher-rank graph $\Lambda$, via the infinite path space $\Lambda^\infty$ of $\Lambda$. Moreover, we proveExpand
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Separable representations, KMS states, and wavelets for higher-rank graphs
Let $\Lambda$ be a strongly connected, finite higher-rank graph. In this paper, we construct representations of $C^*(\Lambda)$ on certain separable Hilbert spaces of the form $L^2(X,\mu)$, byExpand
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