Journal of Differential Geometry

Non-univalent harmonic maps homotopic to diffeomorphisms

F. T. Farrell, P. Ontaneda, and M. S. Raghunathan

Full-text: Open access

Article information

Source
J. Differential Geom., Volume 54, Number 2 (2000), 227-253.

Dates
First available in Project Euclid: 24 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1214341646

Digital Object Identifier
doi:10.4310/jdg/1214341646

Mathematical Reviews number (MathSciNet)
MR1818179

Zentralblatt MATH identifier
1035.58014

Subjects
Primary: 58E20: Harmonic maps [See also 53C43], etc.
Secondary: 53C24: Rigidity results 57R50: Diffeomorphisms

Citation

Farrell, F. T.; Ontaneda, P.; Raghunathan, M. S. Non-univalent harmonic maps homotopic to diffeomorphisms. J. Differential Geom. 54 (2000), no. 2, 227--253. doi:10.4310/jdg/1214341646. https://projecteuclid.org/euclid.jdg/1214341646


Export citation

References

  • [1] S. I. Al'ber, Spaces of mappings into manifold of negative curvature, Dokl. Akad. Nauk. SSSR 178 (1968) 13-16.
  • [2] E. Artin and J. Tate, Classfield theory, Benjamin, 1968.
  • [3] D. Birkes, Orbits of linear algebraic groups, Ann. of Math. 93 (1971) 459-475.
  • [4] A. Borei and Harish-Chandra, Arthmetic subgroups of algebraic groups, Ann. of Math. 75 (1962) 485-535.
  • [5] C. Chevalley, Deux Théorimes d'arithmatiques, J. Math. Soc. Japan 3 (1951) 36-44.
  • [6] K. Corlette, Archimedean superrigidity and hyperbolic geometry, Ann. of Math. 135 (1992) 165-182.
  • [7] J. Eells and L. Lemaire, Selected topics in harmonic maps, CBMS Regional Conf. Ser. 50, Amer. Math. Soc, Providence, RI, 1983.
  • [8] J. Eells and J.H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964) 109-160.
  • [9] F. T. Farrell and L. E. Jones, Negatively curved manifolds with exotic smooth structures, J. Amer. Math. Soc. 2 (1989) 899-908.
  • [10] F. T. Farrell and L. E. Jones, Some non-homeomorphic harmonic homotopy equivalences, Bull. London Math. Soc. 28 (1996) 177-180.
  • [11]F. T. Farrell, L. E. Jones and P. Ontaneda, Hyperbolic manifolds with negatively curved exotic triangulations in dimensions larger than five, J. Differential Geom. 48 (1998) 319-322.
  • [12] F. T. Farrell, Examples of non-homeomorphic harmonic maps between negatively curved manifolds, Bull. London Math. Soc. 30 (1998) 295-296.
  • [13] P. Hartman, On homotopic harmonic maps, Canad. J. Math. 19 (1967) 673-687.
  • [14] L. Hernandez, Kahler manifolds and 1/4-pinching, Duke Math. J. 62 (1991) 601-611.
  • [15] J. Jost and S.-T. Yau, Harmonie maps and superrigidity, Proc. Sympos. Pure Math. 54 (Amer. Math. Soc, Providence, R.I., 1993), 245-280.
  • [16] R. C. Kirby and L. C. Siebenmann, Foundational essays on topological manifolds, smoothings, and triangulations, Ann. of Math. Stud. No. 88 Princeton Univ. Press, Princeton, 1977.
  • [17] M. Kneser, Lectures on Galois cohomology of classical groups, Lecture Notes, Tata Institute, Mumbai.
  • [18] S. Lang, Algebraic number theory, Springer.
  • [19] J.J. Millson and M.S. Raghunathan, Geometric construction of cohomology of arithmetic groups. I, Proc. Indian Acad. Sci. 90 (1981) 103-123.
  • [20] N. Mok, Y.-T. Siu and S.-K. Yeung, Geometric superrigidity, Invent. Math. 113 (1993) 57-83.
  • [21] P. Ontaneda, Hyperbolic manifolds with negatively curved exotic triangulations in dimension six, J. Differential Geom. 40 (1994) 7-22.
  • [22] V. P. Platonov, The problem of strong approximation and the Kneser-Tits conjecture for algebraic groups, Math. USSR Izvestiya 3 (1969) 1139-1147.
  • [23] V. P. Platonov and Rapinchuk, Algebraic Groups and Number Theory, Academic Press, 1994.
  • [24] M. S. Raghunathan, Discrete subgroups of Lie groups, Springer, 1972.
  • [25] M. S. Raghunathan, The Congruence subgroup problem, Proc. Hyderabad Conf. Algebraic Groups, Manoj Prakshan, (India), 465-494.
  • [26] Rohlfs and J. Schwermer, Intersection number of special cycles, J. Amer. Math. Soc. 6 (1993) 755-778.
  • [27] J. Sampson, Some properties and applications of harmonic mappings, Ann. Sci. École Norm. Sup. 11 (1978) 211-228.
  • [28] M. Scharlemann and L. Siebenmann, The Hauptvermutung for smooth singular homeomorphisms, Manifolds Tokyo 1973, (University of Tokyo Press, Tokyo, 1975), 85-91.
  • [29] R. Schoen and S.-T. Yau, On univalent harmonic maps between surfaces, Invent. Math. 44 (1978) 265-278.
  • [30] Y.-T. Siu, The complex-analyticity of harmonic maps and the strong rigidity of compact Kahler manifolds, Ann. of Math. 112 (1980) 73-111.
  • [31] C.W. Stark, Surgery theory and infinite fundamental groups, Ann. of Math. Vol. 1, No. 145, 275-305, Princeton Univ. Press, Princeton, NJ, 2000.
  • [32] S.-T. Yau, Seminar on differential geometry, Ann. of Math. Stud., No. 102, Princeton Univ. Press, Princeton, NJ, 1982.
  • [33] S.-T. Yau and F. Zheng, Negatively 1/4-pinched riemannian metric on a compact Kahler manifold, Invent. Math. 103 (1991) 527-535.