On a Hitchin–Thorpe inequality for manifolds with foliated boundaries
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Atiyah, M.F., Bott, R.: A Lefschetz fixed point formula for elliptic complexes. II. Applications. Ann. Math. 2(88), 451–491 (1968)
Anderson, M.T., Kronheimer, P.B., LeBrun, C.: Complete Ricci-flat Kähler manifolds of infinite topological type. Comm. Math. Phys. 125(4), 637–642 (1989)
Atiyah, M.F., Patodi, V.K., Singer, I.M.: Spectral asymmetry and Riemannian geometry. I. Math. Proc. Cambridge Philos. Soc. 77, 43–69 (1975)
Atiyah, M.F., Patodi, V.K., Singer, I.M.: Spectral asymmetry and Riemannian geometry. II. Math. Proc. Cambridge Philos. Soc. 78(3), 405–432 (1975)
Arthur, L.: Besse. Einstein Manifolds. Reprint of the 1987 edition. Berlin: Springer, reprint of the 1987 edition edition (2008)
Dai, X., Wei, G.: Hitchin–Thorpe inequality for noncompact Einstein 4-manifolds. Adv. Math. 214(2), 551–570 (2007)
Dai, X., Zhang, W.P.: Circle bundles and the Kreck–Stolz invariant. Trans. Am. Math. Soc. 347(9), 3587–3593 (1995)
Etesi, G., Szabó, S.: Harmonic functions and instanton moduli spaces on the multi-Taub-NUT space. Comm. Math. Phys. 301(1), 175–214 (2011)
Gibbons, G.W., Hawking, S.W.: Classification of gravitational instanton symmetries. Comm. Math. Phys. 66(3), 291–310 (1979)
Gilkey, P.B.: Invariance Theory, the Heat Equation, and the Atiyah–Singer Index theorem. Studies in Advanced Mathematics., 2nd edn. CRC Press, Boca Raton (1995)
Gell-Redman, J., Rochon, F.: Hodge cohomology of some foliated boundary and foliated cusp metrics. Math. Nachr. 288(2–3), 206–223 (2015)
Gromov, M.: Volume and bounded cohomology. Inst. Hautes Études Sci. Publ. Math. 56, 5–99 (1983) (1982)
Kotschick, D.: On the Gromov–Hitchin–Thorpe inequality. C. R. Acad. Sci. Paris Sér. I Math. 326(6), 727–731 (1998)
Kotschick, D.: Entropies, volumes, and Einstein metrics. In: Global differential geometry, vol 17 of Springer Proc. Math., pp. 39–54. Springer, Heidelberg (2012)
LeBrun, C.: Complete Ricci-flat Kähler Metrics on $${\bf C}^n$$ C n Need Not be Flat. In: Several complex variables and complex geometry, Part 2 (Santa Cruz, CA, 1989), vol 52 of Proc. Sympos. Pure Math., pp. 297–304. Amer. Math. Soc., Providence, RI (1991)
Lawson, H.B., Jr., Michelsohn, M.L.: Spin Geometry, vol 38 of Princeton Mathematical Series. Princeton University Press, Princeton (1989)
Mazzeo, R., Melrose, R.B.: Pseudodifferential Operators on Manifolds with Fibred Boundaries. Asian J. Math. 2(4), 833–866 (1998). Mikio Sato: a great Japanese mathematician of the twentieth century
Rochon, F.: Pseudodifferential operators on manifolds with foliated boundaries. J. Funct. Anal. 262(3), 1309–1362 (2012)
Sambusetti, A.: An obstruction to the existence of Einstein metrics on $$4$$ 4 -manifolds. Math. Ann. 311(3), 533–547 (1998)
Singer, I.M., Thorpe, J.A.: The Curvature of $$4$$ 4 -Dimensional Einstein Spaces. Global Analysis (Papers in Honor of K. Kodaira), pp. 355–365. Univ. Tokyo Press, Tokyo (1969)
Vaillant, B.: Index- and spectral theory for manifolds with generalized fibred cusps. Bonner Mathematische Schriften [Bonn Mathematical Publications], 344. Universität Bonn, Mathematisches Institut, Bonn: Dissertation. Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn (2001)