@article{AzzaliWahl2019,
  author    = {Azzali, Sara and Wahl, Charlotte},
  title     = {Two-cocycle twists and Atiyah-Patodi-Singer index theory},
  series = {Mathematical Proceedings of the Cambridge Philosophical Society},
  volume    = {167},
  journal   = {Mathematical Proceedings of the Cambridge Philosophical Society},
  number    = {3},
  publisher = {Cambridge Univ. Press},
  address   = {New York},
  issn      = {0305-0041},
  doi       = {10.1017/S0305004118000427},
  pages     = {437 -- 487},
  year      = {2019},
  abstract  = {We construct eta- and rho-invariants for Dirac operators, on the universal covering of a closed manifold, that are invariant under the projective action associated to a 2-cocycle of the fundamental group. We prove an Atiyah-Patodi-Singer index theorem in this setting, as well as its higher generalisation. Applications concern the classification of positive scalar curvature metrics on closed spin manifolds. We also investigate the properties of these twisted invariants for the signature operator and the relation to the higher invariants.},
  language  = {en}
}
@article{AzzaliPaycha2020,
  author    = {Azzali, Sara and Paycha, Sylvie},
  title     = {Spectral zeta-invariants lifted to coverings},
  series = {Transactions of the American Mathematical Society},
  volume    = {373},
  journal   = {Transactions of the American Mathematical Society},
  number    = {9},
  publisher = {American Mathematical Society},
  address   = {Providence, RI},
  issn      = {0002-9947},
  doi       = {10.1090/tran/8067},
  pages     = {6185 -- 6226},
  year      = {2020},
  abstract  = {The canonical trace and the Wodzicki residue on classical pseudo-differential operators on a closed manifold are characterised by their locality and shown to be preserved under lifting to the universal covering as a result of their local feature. As a consequence, we lift a class of spectral zeta-invariants using lifted defect formulae which express discrepancies of zeta-regularised traces in terms of Wodzicki residues. We derive Atiyah's L-2-index theorem as an instance of the Z(2)-graded generalisation of the canonical lift of spectral zeta-invariants and we show that certain lifted spectral zeta-invariants for geometric operators are integrals of Pontryagin and Chern forms.},
  language  = {en}
}
@article{AzzaliGoetteSchick2015,
  author    = {Azzali, Sara and Goette, Sebastian and Schick, Thomas},
  title     = {Large time limit and local L-2-index theorems for families},
  series = {Journal of noncommutative geometry},
  volume    = {9},
  journal   = {Journal of noncommutative geometry},
  number    = {2},
  publisher = {EMS Publ.},
  address   = {Z{\"u}rich},
  issn      = {1661-6952},
  doi       = {10.4171/JNCG/203},
  pages     = {621 -- 664},
  year      = {2015},
  abstract  = {We compute explicitly, and without any extra regularity assumptions, the large time limit of the fibrewise heat operator for Bismut-Lott type superconnections in the L-2-setting. This is motivated by index theory on certain non-compact spaces (families of manifolds with cocompact group action) where the convergence of the heat operator at large time implies refined L-2-index formulas. As applications, we prove a local L-2-index theorem for families of signature operators and an L-2-Bismut-Lott theorem, expressing the Becker-Gottlieb transfer of flat bundles in terms of Kamber-Tondeur classes. With slightly stronger regularity we obtain the respective refined versions: we construct L-2-eta forms and L-2-torsion forms as transgression forms.},
  language  = {en}
}
@article{AntoniniAzzaliSkandalis2016,
  author    = {Antonini, Paolo and Azzali, Sara and Skandalis, Georges},
  title     = {Bivariant K-theory with R/Z-coefficients and rho classes of unitary representations},
  series = {Journal of functional analysis},
  volume    = {270},
  journal   = {Journal of functional analysis},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0022-1236},
  doi       = {10.1016/j.jfa.2015.06.017},
  pages     = {447 -- 481},
  year      = {2016},
  abstract  = {We construct equivariant KK-theory with coefficients in and R/Z as suitable inductive limits over II1-factors. We show that the Kasparov product, together with its usual functorial properties, extends to KK-theory with real coefficients. Let Gamma be a group. We define a Gamma-algebra A to be K-theoretically free and proper (KFP) if the group trace tr of Gamma acts as the unit element in KKR Gamma (A, A). We show that free and proper Gamma-algebras (in the sense of Kasparov) have the (KFP) property. Moreover, if Gamma is torsion free and satisfies the KK Gamma-form of the Baum-Connes conjecture, then every Gamma-algebra satisfies (KFP). If alpha : Gamma -> U-n is a unitary representation and A satisfies property (KFP), we construct in a canonical way a rho class rho(A)(alpha) is an element of KKR/Z1,Gamma (A A) This construction generalizes the Atiyah-Patodi-Singer K-theory class with R/Z-coefficients associated to alpha. (C) 2015 Elsevier Inc. All rights reserved.},
  language  = {en}
}