References
Allard, W.: Analytic proofs of the index theorem. (in preparation)
Ash, A., Mumford, D., Rapoport, M., Tai, Y.: Smooth compactification of locally symmetric varieties. Brookline, Mass.: Math. Sci. Press, 1975
Atiyah, M.F., Bott, R., Patodi, V.K.: On the heat equation and the index theorem. Invent. Math.19, 279–330 (1973)
Atiyah, M.F., Bott, R., Shapiro, A.: Clifford modules. Topology3, 3–38 (1964)
Atiyah, M.F., Donnelly, H., Singer, I.M.: Eta invariants, signature defects of cusps, and values ofL-functions. Ann. Math.118, 131–177 (1983)
Atiyah, M.F., Patodi, V.K., Singer, I.M.: Spectral asymmetry and Riemannian geometry I. Math. Proc. Camb. Philos. Soc.77, 43–69 (1975)
Baily, W.L., Jr., Borel, A.: Compactification of arithmetic quotients of bounded symmetric domains. Ann. Math.84, 442–528 (1966)
Barbasch, D., Moscovici, H.:L 2-Index and the Selberg trace formula. J. Funct. Anal.53, 151–201 (1983)
Bellman, R.E.: A brief introduction to theta functions. New York: Holt, Rinehart and Winston, 1961
Borel, A.: Stable real cohomology of arithmetic groups. Ann. Sci. Ec. Norm. Super., IV. Ser.7, 235–272 (1974)
Borel, A.:L 2-cohomology and intersection cohomology of certain arithmetic varieties. In: Emmy Noether in Bryn Mawr. Berlin-Heidelberg-New York: Springer 1983
Borel, A., Casselman, W.:L 2-cohomology of locally symmetric manifolds of finite volume. Duke Math. J.50, 625–647 (1983)
Borel, A., Casselman, W.: Cohomologie d'intersection de varieties arithmetiques de rang rationnel 2. Comtes Rendus301, 369–373 (1985)
Borel, A., Serre, J.-P.: Corners and arithmetic groups. Comment. Math. Helv.48, 244–297 (1974)
Callias, C.: Axial anomalies and index theorems on open spaces. Commun. Math. Phys.62, 213–234 (1978)
Callias, C., Taubes, C.: Functional determinants in Yang-Mills theory. Commun. Math. Phys.77, 229–250 (1980)
Cheeger, J., Goresky, M., MacPherson, R.:L 2-cohomology and intersection homology of singular algebraic varieties. In: Yau, S.-T. (ed.), Seminar on differential geometry, pp. 303–340. Princeton, N.J.: Princeton University Press 1982
Chernoff, P.: Essential self-adjointness of powers of generators of hyperbolic equations. J. Funct. Anal.12, 401–414 (1973)
Conway, J.: A course in functional analysis. New York: Springer 1985
Donnelly, H.: On the cuspidal spectrum for finite volume symmetric spaces. J. Differ. Geom.17, 239–253 (1982)
Donnelly, H., Li, P.: Pure point spectrum and negative curvature for noncompact manifolds. Duke Math. J.46, 497–503 (1979)
Fedosov, B.V.: Analytic formulas for the index of elliptic operators. Trans. Moscow Math. Soc.30, 159–240 (1974)
Gelfand, I.M., Vilenkin N.: Generalized functions, Vol. 4: Applications of harmonic analysis. New York: Academic Press 1964
Getzler, E.: Pseudodifferential operators on supermanifolds and the Atiyah-Singer index theorem. Commun. Math. Phys.92, 163–178 (1983)
Gromov, M., Lawson, B.: Positive scalar curvature and the Dirac operator on complete Riemannian manifolds. Publ. Math., Inst. Hautes Etud. Sci.58, 83–196 (1983)
Hirzebruch, F.: Hilbert modular surfaces. L'Enseign. Math.19, 183–281 (1973)
Kostant, B.: Lie algebra cohomology and the generalized Borel-Weil theorem. Ann., Math.74, 329–387 (1961)
Kumano-go, H.: Pseudo-Differential Operators. Cambridge, Mass: M.I.T. Press 1981
Matsushima, Y., Murakami, S.: On vector bundle valued harmonic forms and automorphic forms on symmetric Riemannian manifolds. Ann. Math.78, 417–449 (1963)
Millson, J.: Closed geodesics and the η-invariant. Ann. Math.108, 1–39 (1978)
Moscovici, H.:L 2-index of elliptic operators on locally symmetric spaces of finite volume. In: Operator algebras andK-theory. Contemp. Math.10, 129–138 (1982)
Moscovici, H.: The signature with local coefficients of locally symmetric spaces. Tôhoku Math. J.37, 513–522 (1985)
Mueller, W.: Signature defects of cusps of Hilbert modular varieties. J. Differ. Geom.20, 55–119 (1984)
Patodi, V.K.: Curvature and the eigenforms of the Laplace operator. J. Differ. Geom.5, 233–249 (1971)
Saper, L., Stern, M.:L 2-cohomology of arithmetic, varieties. Ann. Math. (to appear)
Stern, M.:L 2-index theorems on warped products. Princeton University Ph.D. thesis, October 1984
Zucker, S.:L 2-cohomology of warped products and arithmetic groups. Invent. Math.70, 169–218 (1982)
Zucker, S.:L 2-cohomology and intersection homology of locally symmetric varieties, II. Compos. Math.59, 339–398 (1986)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Stern, M. L 2-index theorems on locally symmetric spaces. Invent Math 96, 231–282 (1989). https://doi.org/10.1007/BF01393964
Issue Date:
DOI: https://doi.org/10.1007/BF01393964