Preprints and Recent Papers
  • Stability of L2 invariants on stratified spaces (with Francesco Bei and Boris Vertman)
    Preprint October 2023., 31pp. To appear in Int. Math. Res. Notices.
     
  • Heat kernels of perturbed operators and index theory on G-proper manifolds (with Hessel Posthuma, Yanli Song and Xiang Tang)
    Preprint July 2023., 29pp.
     
  • Primary and secondary invariants of Dirac operators on G-proper manifolds (with Xiang Tang)
    Preprint April 2022, 39pp. Proceedings of Symposia in Pure Mathematics. Volume 105, 2023.
     
  • Higher orbital integrals, rho numbers and index theory (with Hessel Posthuma, Yanli Song, Xiang Tang)
    Preprint August 2021. NEW VERSION: July 2023. 49pp. Submitted.
     
  • Positive scalar curvature on simply connected spin pseudomanifolds (with Boris Botvinnik and Jonathan Rosenberg)
    Journal of Topology and Analysis. 15 (2023), n. 2, 413-444.
     
  • Mapping analytic surgery to homology, higher rho numbers and metrics of positive scalar curvature (with Thomas Schick and Vito Felice Zenobi)
    Preprint May 2019, 48pp. NEW VERSION: February 2021 (103 pp). To appear in Memoirs AMS.
     
  • Stratified surgery and K-theory invariants of the signature operator (with P. Albin)
    Ann. Sci. Ecole Normale Superieure. (4) 55 (2022), no. 1, 43 - 110.
     
  • Higher genera for proper actions of Lie groups, Part 2: the case of manifolds with boundary (with Hessel Posthuma)
    Annals of K-Theory, vol 6, 2021, n. 4, 713-782.
     
  • Positive scalar curvature on spin pseudomanifolds: the fundamental group and secondary invariants (with Boris Botvinnik and Jonathan Rosenberg)
    SIGMA (Symmetry, Integrability and Geometry: Methods and Applications), vol 17, 2021, 39pp.
     
  • Signatures of Witt spaces with boundary (with Boris Vertman).
    Advances in Mathemathics. 405 (2022), Paper No. 108448, 80 pp.
     
  • A note on higher Todd genera of complex manifolds (with Francesco Bei)
    Rendiconti di Matematica e delle sue applicazioni, vol. 42, 2021, 49-60.
     
  • On positive scalar curvature bordism (with Thomas Schick and Vito Felice Zenobi)
    Preprint December 2019, 8pp. To appear in Communications in Analysis and Geometry.
     
  • On analytic Todd classes of singular varieties (with F. Bei)
    International Mathematics Research Notices, 19, 2021, 14840-14881.
     
  • Singular spaces, groupoids and metrics of positive scalar curvature (with V. F. Zenobi)
    Journal of Geometry and Physics, vol 137, 2019, 87-123.
     
  • Higher genera for proper actions of Lie groups (with H. Posthuma)
    Annals of K-Theory, vol 3, 2019, 473-504.
     
  • Eta and rho invariants on manifolds with edges (with B. Vertman)
    Annales de l'Institut Fourier, vol 69, 2019, 1955-2035.
     
  • On the $L^2$-$\overline{\partial}$-cohomology of Saper metrics (with F. Bei)
    Mathematische Zeitschrift, Vol. 290 (2018), pp 521-537.
     
  • A note on the higher Atiyah-Patodi-Singer index theorem on Galois coverings (with A. Gorokhovsky and H. Moriyoshi)
    Journal of non commutative geometry (2016), vol. 10, issue 1, pp 265-306.
     
  • The surgery exact sequence, K-theory and the signature operator (with T. Schick)
    Annals of K-Theory 1-2 (2016), 109--154. DOI 10.2140/akt.2016.1.109
     
  • Refined intesection homology on non-Witt spaces (with P. Albin, M. Banagl, E. Leichtnam and R. Mazzeo)
    Journal of Analysis and Topology 2015. Doi: 10.1142/S1793525315500065.
     
  • The Novikov conjecture on Cheeger spaces (with P. Albin, E. Leichtnam and R. Mazzeo)
    Journal of non commutative geometry (2017), Vol 11, pp 451-506.
     
  • Hodge theory on Cheeger spaces (with P. Albin, E. Leichtnam and R. Mazzeo)
    Journal fur die Reine und Angewndte Mathematik (Crelle's Journal) ISSN (Online) 1435-5345. February 2016
     
  • Rho classes, index theory and Stolz' positive scalar curvature sequence (with Thomas Schick)
    Journal of Topology. Vol. 7. 2014 pp. 965-1004
     
  • Eta cocycles, relative pairings and the Godbillon-Vey index theorem. (with Hitoshi Moriyoshi).
    GAFA Volume 22, Issue 6 (2012). 107pp.
    This is the complete article corresponding to the announcement
    "Eta cocycles" by the same authors (arXiv:0907.0173).
     
  • The signature package on Witt spaces. (with Pierre Albin, Eric Leichtnam and Rafe Mazzeo).
    Ann. Sci. Ecole Normale Superieure. Tome 45, 2012. 70pp.
     
  • Eta cocycles (with Hitoshi Moriyoshi).
    Pubblished as "Relative pairings and the Atiyah-Patodi-Singer index formula for the Godbillon-Vey cocycle".
    In the volume "Noncommutative Geometry and Global Analysis", p. 225-247, Contemporary Mathematics Vol 546, 2011.
     
  • Index, eta and rho invariants on foliated bundles (with Moulay Benameur).
    Asterisque vol 327, p. 201-287, 2009.
     
  • The index of Dirac operators on manifolds with fibered boundary(with E. Leichtnam and R. Mazzeo).
    Bull. Belgian Mathematical Society Vol 13. n. 5
    (Proceedings of the Joint BeNeLuxFra Conference in Mathematics, Ghent, 2005).
     
  • Groups with torsions, bordism and rho-invariants(with T. Schick).
    Pacific Journal of Mathematics. Vol 232 (20007)
     
  • Bordism, rho-invariants and the Baum-Connes conjecture(with T. Schick).
    Journal of Noncommutative Geometry. Vol 1. n. 1. (2007)
     
  • Cut-and-Paste on foliated bundles (with E. Leichtnam).
    Contemp. Mathem. vol. 366 (2005) pp 351-392 "Spectral Geometry of Manifolds with Boundary",
    Amer. Math. Soc., Providence, RI.
    ed. by B. Booss-Bavnbek, G. Grubb and K. P. Wojciechowski.
     
  • Etale groupoids, eta invariants and index theory (with E. Leichtnam).
    Journal fur die Reine und Angewndte Mathematik (Crelle's Journal) Vol 587 (2005) pp. 169 - 233
     
  • Elliptic operators and higher signatures (with E. Leichtnam).
    Ann. Inst. Fourier vol. 54 (2004) pp. 1197-1277
     
  • Dirac index classes and the noncommutative spectral flow (with E. Leichtnam).
    Journal of Functional Analaysis.     200 (2003)
     
  • On higher eta invariants and metrics of positive scalar curvature (with E. Leichtnam).
    K-Theory.     24 (2001)
     
  • On the homotopy invariance of higher signatures on manifolds with boundary
    (with E. Leichtnam and J. Lott) ,  Journal of Differential Geometry. 54 (2000).
     
  •  A higher Atiyah-Patodi-Singer index theorem for the signature operator on Galois coverings
    with E. Leichtnam), Annals of Global Analysis and Geometry, 19 (1999).
     
  • Homotopy invariance of twisted higher signatures on manifolds with boundary
    (with E. Leichtnam), Bulletin de la Societe Matematique de France, 127 (1999).
     
  •  Spectral sections and higher Atiyah-Patodi-Singer index theory
    (with E. Leichtnam), Geometric and Functional Analysis (GAFA), 8 (1998).
     
  • The b-pseudodifferential calculus on Galois coverings and a higher Atiyah-Patodi-Singer index theorem
    (with E. Leichtnam) , Memoires de la Societe Mathematique de France,n. 68 (1997).
    This article has obtained a Featured Review in the issue 99dof Mathematical Reviews of the AMS.
     
  • Dirac operators, heat kernels and microlocal analysis. Part I: Family index theory
    Rendiconti del Circolo Matematico di Palermo, Supplemento, Serie II, 49, 1997.
     
  • Dirac operators, heat kernels and microlocal analysis. Part II: Analytic surgery
    (with R. Mazzeo), Rendiconti di Matematica e delle sue applicazioni (Roma), 18 (1998).
     
  • An index theorem on odd dimensional manifolds with boundary (with R. Melrose).
    Journal of Differential Geometry , 46 n.2 (1997)
     
  • Families of Dirac operators, boundaries and the b-calculus
    (with R. Melrose), Journal of Differential Geometry, 46 n. 1 (1997).
    This article has obtained a Featured Review in the issue 99a of Mathematical Reviews of the AMS.