Journal of Differential Geometry

Novikov's higher signature and families of elliptic operators

Gheorghe Lusztig

Full-text: Open access

Article information

Source
J. Differential Geom., Volume 7, Number 1-2 (1972), 229-256.

Dates
First available in Project Euclid: 25 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1214430829

Digital Object Identifier
doi:10.4310/jdg/1214430829

Mathematical Reviews number (MathSciNet)
MR0322889

Zentralblatt MATH identifier
0265.57009

Subjects
Primary: 57D65
Secondary: 57D20 58G10

Citation

Lusztig, Gheorghe. Novikov's higher signature and families of elliptic operators. J. Differential Geom. 7 (1972), no. 1-2, 229--256. doi:10.4310/jdg/1214430829. https://projecteuclid.org/euclid.jdg/1214430829


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References

  • [1] M. F. Atiyah, The signature of fibre bundles, Global Analysis, papers in honor of K. Kodaira, Princeton University Press, Princeton, 1969, 73-84.
  • [2] M. F. Atiyah and I. M. Singer, The index of elliptic operators. III, Ann. of Math. 87 (1968) 546-604.
  • [3] M. F. Atiyah and I. M. Singer, The index of elliptic operators. IV, Ann. of Math. 93 (1971) 119-138.
  • [4] S. S. Chern, F. Hirzebruch and J. P. Serre, On the index of a fibered manifold, Proc. Amer. Math. Soc. 8 (1957) 587-596.
  • [5] I. M. Gelfand and A. S. Miscenko, Quadratic forms over commutative group rings and K-theory, Funkcional. Anal. i Prilozen 3 (1969) 28-33, (Russian).
  • [6] W. C. Hsiang, A splitting theorem and the Kunneth formula in algebraic K-theory, Algebraic K-theory and its geometric applications, Lecture Notes in Math. Vol. 108, Springer, Berlin, 1969, 72-77.
  • [7] G. G. Kasparov, On the homotopy invariance of rational Pontrjagin numbers Dokl. Akad. Nauk SSSR 190 (1970) 1022-1025, (Russian).
  • [8] K. Kodaira, Characteristic linear systems of complete continuous systems, Amer. J. Math. 78 (1956) 716-744.
  • [9] Y. Matsushima, On Betti numbers of compact locally symmetric riemannian manifolds, Osaka Math. J. 14 (1962) 1-20.
  • [10] A. S. Miscenko, Homotopy invariants of non-simply connected manifolds. I. Rational invariants, Izv. Akad. Nauk SSSR Ser. Mat. 34 (1970) 501-514, (Russian).
  • [11] S. P. Novikov, On manifolds with free abelian fundamental group and their applications, Izv. Akad. Nauk SSSR Ser. Mat. 30 (1966) 207-246, (Russian).
  • [12] S. P. Novikov, Pontrjagin classes, the fundamental group and some problems in stable algebra, Essays on Topology and Related Topics, Memoires dedies a G. de Rham, Springer, Berlin, 1969, 147-155.
  • [13] S. P. Novikov, Algebraic construction and properties of Hermitian analogues of K-theory...., Izv. Akad. Nauk SSSR Ser. Mat. 34 (1970) 253-288, (Russian).
  • [14] V. A. Rohlin, Pontrjagin-Hirzebruch classes in codimension 2, Izv. Akad. Nauk SSSR Ser. Mat. 30 (1966) 705-718, (Russian).
  • [15] G. Segal, Fredholm complexes, Quart. J. Math. Oxford Ser. 21 (1970) 385-402.