Skip to main content
Log in

On homotopy invariance of higher signatures

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  • B 1. Bieri, R.: A group with torsion-free 2-divisible homology and Cappell's result on the Novikov Conjecture. Inventiones math.33, 181–184 (1976)

    Google Scholar 

  • B. Browder, W.: Surgery on simply connected manifolds. Berlin-Heidelberg-New York Springer 1972

    Google Scholar 

  • C 1. Cappell, S. E.: A splitting theorem for manifolds. Inventiones math.33, 69–170 (1976)

    Google Scholar 

  • C 2. Cappell, S. E.: On connected sum of manifolds. Topology13, 395–400 (1974)

    Google Scholar 

  • C 3. Cappell, S. E.: Manifold with fundamental group a generalized free product I. Bull. Amer. Math. Soc.80, 1193–1198 (1974)

    Google Scholar 

  • C 4. Cappell, S. E.: Unitary nilpotent groups and HermitianK-theory. Bull. Amer. Math. Soc.80, 1117–1122 (1974)

    Google Scholar 

  • CS. Cappell, S. E., Shaneson, J. L.: The codimension two placement problem and homology equivalent manifolds. Ann. of Math.99, 277–348 (1974)

    Google Scholar 

  • ES. Eilenberg, S., Steenrod, N.: Foundations of algebraic topology. Princeton: Princeton University Press 1952

    Google Scholar 

  • FH. Farrell, F. T., Hsiang, W. C.: Manifolds with μ1 = Z 00D7;α G. Amer. J. Math.95, 813–848 (1973)

    Google Scholar 

  • H 1. Haken, W.: Theorie der Normalflachen. Acta Math.105, 245–375 (1961)

    Google Scholar 

  • H 2. Hirzebruch, F.: Topological methods in algebraic geometry (3rd ed.) Berlin-Heidelberg-New York: Springer 1966

    Google Scholar 

  • H 3. Hsiang, W. C.: A splitting theorem and the Künneth formula in algebraicK-theory. In: AlgebraicK-theory and its geometric applications. Lecture Notes in Mathematics No.108, pp. 72–77. Berlin-Heidelberg-New York: Springer 1969

    Google Scholar 

  • K. Kasparov, G. G.: On the homotopy invariance of rational Pontrjagin numbers (Russian). Dokl. Akad. Nauk SSSR190, 1022–1025 (1970)

    Google Scholar 

  • KS 1. Kirby, R. C., Siebenmann, L. C.: On the triangulation of manifolds and the hauptvermutung, Bull. Amer. Math. Soc.75, 742–749 (1969) (See also Foundations of Topology, Not. Amer. Math. Soc.16, 848 (1969))

    Google Scholar 

  • Ka. Kahn, P.: Characteristic numbers and oriented homotopy type. Topology3, 81–95 (1965)

    Google Scholar 

  • KS 2. Kwun, K. W., Szczarba, R.: Product and sum theorems for Whitehead torsion. Ann. of Math.82, 183–190 (1965)

    Google Scholar 

  • L. Lusztig, G.: Novikov's higher signature and families of elliptic operators. J. of Diff. Geometry7, pp. 229–256 (1972)

    Google Scholar 

  • M. Milnor, J. W.: Differentiable manifolds which are homotopy spheres. Notes, Princeton University, 1959

  • N 1. Novikov, S. P.: On manifolds with free abelian fundamental group and their application (Russian). Izv. Akad. Nauk SSSR Ser. Mat.30, 207–246 (1966)

    Google Scholar 

  • N 2. Novikov, S. P.: Pontrjagin classes, the fundamental group and some problems in stable algebra. In: Essays on topology and related topics. Memoirs dédiés à G. de Rham, pp. 147–155. Berlin-Heidelberg-New York: Springer 1969

    Google Scholar 

  • Q. Quinn, F.: B TOPn and the surgery obstruction. Bull. Amer. Math. Soc. 1972

  • R. Rohlin, V. A.: Pontrjagin-Hirzebruch classes in codimension two (Russian). Izv. Akad. Nauk SSSR Ser. Mat.30, 705–718 (1966)

    Google Scholar 

  • S 1. Shaneson, J. L.: Wall's surgery obstruction groups forZ×G. Ann. of Math.90, 269–334 (1969)

    Google Scholar 

  • S 2. Sullivan, D.: Triangulating and smoothing homotopy equivalences and homeomorphisms. Geometric topology seminar notes, Princeton University, 1967

  • W 1. Waldhausen, F.: Whitehead groups of generalized free products, Mimeographed preprint

  • W 2. Wall, C. T. C.: Surgery of compact manifolds. London-New York: Academic Press 1970

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

The author is an A. P. Sloan fellow and was partially supported by an NSF grant. This paper was written at the Institut der hautes Etudes Scientifiques in 1973. The author wishes to thank the Institut for its hospitality.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cappell, S.E. On homotopy invariance of higher signatures. Invent Math 33, 171–179 (1976). https://doi.org/10.1007/BF01402341

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01402341

Keywords

Navigation