Preprints and Publications

• with J. Nordström: Nu-invariants of extra-twisted connected sums, with an appendix by D. Zagier, preprint (2020); arXiv:2010.16367 [math.GT]
• with M. Kerin and K. Shankar: Highly connected 7-manifolds, the linking form and non-negative curvature, preprint (2020); arXiv:2003.04907 [math.DG].
• with D. Crowley, and J. Nordström: An analytic invariant of G₂ manifolds, preprint (2015); arXiv:1505.02734 [math.GT].
• Analytic Torsion for Families, lectures held at the workshop "Smooth Fibre Bundles and Higher Torsion Invariants" at Göttingen 2003, preprint (2004) (dvi, ps.gz).
• Morse theory and higher torsion invariants II, preprint (2003) (dvi, ps.gz); arXiv:math/0305287.
• Morse theory and higher torsion invariants I, preprint (2001) (dvi, ps.gz); arXiv:math/0111222.

• with M. Kerin and K. Shankar: Highly connected 7-manifolds and non-negative curvature, Ann. of Math. (2) 191 (2020), 829-892,
  DOI: 10.4007/annals.2020.191.3.3, arXiv:1705.05895 [math.DG].
• with S. Azzali, T. Schick, Large time limit and local L²-index theorems for families, J. Noncomm. Geom. 9 (2015), 621-664,
  DOI: 10.4171/JNCG/203, arXiv:1306.5659 [math.DG].
• Adiabatic limits of Seifert fibrations, Dedekind sums, and the diffeomorphism type of certain 7-manifolds, J. Eur. Math. Soc. 16 (2014), 2499-2555 DOI: 10.4171/JEMS/492, arXiv:1108.5614 [math.DG].
• with K. Igusa, Exotic smooth structures on topological fibre bundles II, Trans. Amer. Math. Soc. 366 (2014), 791-832 DOI: 10.1090/S0002-9947-2013-05858-8, arXiv:1011.4653 [math.KT].
• with K. Igusa, B. Williams, Exotic smooth structures on topological fibre bundles I, Trans. Amer. Math. Soc. 366 (2014), 749-790 DOI: 10.1090/S0002-9947-2013-05857-6, arXiv:1203.2203 [math.KT].
• with D. Crowley: Kreck-Stolz invariants for quaternionic line bundles, Trans. Amer. Math. Soc. 365 (2013), 3193-3225 DOI: 10.1090/S0002-9947-2012-05732-1, arXiv:1012.5237 [math.GT].
• Scalar Curvature Estimates by Parallel Alternating Torsion, Trans. of the Amer. Math. Soc. 363 (2011), 165-183, DOI: 10.1090/S0002-9947-2010-04878-0, arXiv:0709.4586 [math.DG].
• Eta invariants of homogeneous spaces, Pure Appl. Math. Q. 5 (Friedrich Hirzebruch special issue II; 2009), 915-946, DOI: 10.4310/PAMQ.2009.v5.n3.a2, arXiv:math/0203269.
• with C. Zickert: The Extended Bloch Group and the Cheeger-Chern-Simons Class, Geom. Topol. 11 (2007), 1623-1635, DOI: 10.2140/gt.2007.11.1623, arXiv:0705.0500 [math.GT].
• Vafa-Witten Estimates for Compact Symmetric Spaces, Comm. Math. Phys. 271 (2007), 839-851, DOI: 10.1007/s00220-007-0188-4, arXiv:math/0605269.
• with N. Kitchloo and K. Shankar: Diffeomorphism type of the Berger space SO(5)/SO(3), Am. J. Math. 126 (2004), 395-416, DOI: 10.1353/ajm.2004.0014, arXiv:math/0204352.
• with J.-M. Bismut: Equivariant de Rham torsions, Ann. of Math. 159 (2004), 53-216,
  DOI: 10.4007/annals.2004.159.53, announced in:
  • Torsions analytique équivariantes en théorie de de Rham, C. R. Acad. Sci Paris, t. 332, Série I, p. 33-39, 2001,
    DOI: 10.1016/S0764-4442(00)01772-9.
• with U. Semmelmann: Scalar Curvature Estimates for Compact Symmetric Spaces, Diff. Geom. Appl. 16 (2002), 65-78,>br> DOI: 10.1016/S0926-2245(01)00068-7, arXiv:math/0010199.
• with U. Semmelmann: The Point Spectrum of the Dirac Operator on Noncompact Symmetric Spaces, Proc. Amer. Math. Soc. 130 (2002), 915-923,
  DOI: 10.1090/S0002-9939-01-06158-5; arXiv:math/9903177.
• with J.-M. Bismut: Families torsion and Morse functions, Astérisque 275 (2001), x + 293 pages
  DOI: 10.24033/ast.513, Featured Review 2002h:58059; announced in:
  • Rigidité des formes de torsion analytique en théorie de de Rham, C. R. Acad. Sci Paris, t. 330, Série I, p. 471-477, 2000, DOI: 10.1016/S0764-4442(00)00205-6.
  • Formes de torsion analytique en théorie de de Rham et fonctions de Morse, C. R. Acad. Sci Paris, t. 330, Série I, p. 479-484, 2000
    DOI: 10.1016/S0764-4442(00)00204-4.
• with U. Semmelmann: Spin^c Structures and Scalar Curvature Estimates, Ann. Global Anal. Geom. 20 (2001), 301-324,
  DOI: 10.1023/A:1013035721335, arXiv:math/9905089.
• with J.-M. Bismut: Holomorphic Equivariant Analytic Torsions, Geom. funct. anal. 10 (2001), 1289-1422,
  DOI: 10.1007/PL00001654; announced in:
  • Torsions analytiques équivariantes holomorphes, C. R. Acad. Sci Paris, t. 329, Série I, p. 203-210, 1999
    DOI: 10.1016/S0764-4442(00)88594-8.
• Equivariant eta-Invariants and eta-Forms, J. reine angew. Math. 526 (2000), 181-236,
  DOI: 10.1515/crll.2000.073.
• Equivariant eta-Invariants on Homogeneous Spaces, Math. Z. 232 (1999) 1, 1-42,
  DOI: 10.1007/PL00004757.
• with V. Schroeder: Totally geodesic hypersurfaces in manifolds of nonpositive curvature, manuscripta math. 86 (1995), 169-184,
  DOI: 10.1007/BF02567986.

• with D. Crowley, and J. Nordström: Distinguishing G₂-manifolds, in S. Karigiannis, N. C. Leung, J. Lotay (eds), Lectures and surveys on G₂-manifolds and related topics, Fields Inst. Commun. 84, Springer, New York (2020), 143-172,
  DOI: 10.1007/978-1-0716-0577-6_6, arXiv:1505.05585 [math.DG].
• Computations and Applications of eta Invariants, in C. Bär, J. Lohkamp, M. Schwarz (eds), Global Differential Geometry, Springer Proc. Math. 17, Springer, Heidelberg (2012), 401-431,
  DOI: 10.1007/978-3-642-22842-1_13, arXiv:1011.4766 [math.DG].
• Torsion Invariants for Families, in X. Dai (ed.) et al., From probability to geometry II, Volume in honor of the 60th birthday of Jean-Michel Bismut, Astérisque 328 (2009), 161-206,
  DOI: 10.24033/ast.814, arXiv:0804.3020 [math.DG].
• Äquivariante eta-Invarianten homogener Räume, Dissertation (german), Shaker Verlag, Aachen, ISBN 3-8265-2820-4 (1997), English Summary (dvi, ps), Deutsche Zusammenfassung (dvi, ps).
• Review on "Tristan Needham: Visual differential geometry and forms. A mathematical drama in five acts, Princeton, NJ: Princeton University Press. 2021, xviii, 501 Seiten," in Mathematische Semesterberichte (2024); View.