Skip to main content
SpringerLink
Log in

Class numbers and periodic smooth maps

  • Published:
Commentarii Mathematici Helvetici

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Atiyah, M. F. andBott, R. A Leftshetz fixed point formula for ellitpic complexes: II. Applications, Ann. of Math.88 451–491.

  2. Bredon, G. Representations at fixed points of smooth actions of compact groups, Ann. of Math.89 (1969), 512–532.

    Article  MathSciNet  Google Scholar 

  3. —Introduction to compact transformation groups, Academic Press, New York, 1972.

    Google Scholar 

  4. Cappell, S. E. andShaneson, J. L. Non-linear similarity, Ann. of Math.113 (1981), 315–355.

    Article  MathSciNet  Google Scholar 

  5. —Fixed points of periodic differentiable maps, Inventiones Mathematicae68 (1982), 1–20. (See also Proc. Natl. Acad. Sci. USA77 (1980), 5052–4).

    Article  MathSciNet  Google Scholar 

  6. —Topological rationality of linear representations. Publications Mathématiques de l’Inst. Hautes Etudes Sci.56 (1983), 309–336.

    Google Scholar 

  7. DeRham, G.,Sur les neauveaux invariants topologiques de M. Reidemeister, International Conference of Topology (Moscow, 1935), Recueil Mathematique, Moscow 1936, t. I. (43), 737–743.

    Google Scholar 

  8. —Sur les complexes avec automorphismes, Comment. Math. Helv. (12) 1939, 197–211.

    Article  MathSciNet  Google Scholar 

  9. —,Sur les conditions de homesmorphie de deux rotations de la sphere a n-dimensions et sur les complexes a automorphismes, Colloques Internationaux de Centres National de la Recherche Scientfique (CNRS) Vol. 12, Topologie Algebraique, Paris, 1949, 87–95.

    MathSciNet  Google Scholar 

  10. —Complexes a automorphismes et homeomorphies differentiables, Ann. Inst. Fourier t. II, 1950, 51–67.

    MathSciNet  Google Scholar 

  11. deRham, G.,Reidemeister’s torsion invariant and rotations of S h. Diff. Analysis, Oxford Univ. Press, 1964, 27–36.

  12. Iwasawa, K. A class number formula for cyclotomic fields. Ann. of Math.76 (1962), 171–179.

    Article  MathSciNet  Google Scholar 

  13. Kuiper, N. andRobbin, J. W. Topological classification of linear endomorphisms, Inv. Math.19 (1973), 83–106.

    Article  MathSciNet  Google Scholar 

  14. Kummer, F.,Uber eine Eigenshaft du Einheitern der ano den Wurzeln der Gleichung α -=1gebildelen complexen Zahlen, und uber den zweiten Factor der Klassenzahl. Manatsbericht Konig. Preuss. Akad. der Wiss. 1870 (855–880), Collected Papers Vol. I, Springer Verlag, Berlin, 1975, 919–944.

    Google Scholar 

  15. Lang, S.,Cyclotomic Fields. Springer Verlag, New York, 1978.

    MATH  Google Scholar 

  16. Petrie, T. G-Surgery I, Springer Lecture Notes No. 664, (1978), 196–232.

    MathSciNet  Google Scholar 

  17. Petrie, T.,Three theorems on transformation groups, in “Algebraic Topology, Aarhus 1978,” Springer Lecture Notes No. 763 (1979), 549–572.

  18. Sanchez, C. Actions of groups of odd order on compact orientable manifolds. Proc. Amer. Math. Soc.54 (1976), 445–448.

    Article  MathSciNet  Google Scholar 

  19. Sinnott, W. On the Stickelberger ideal and the circular units of a cyclotomic field, Ann. of Math,108 (1978), 107–134.

    Article  MathSciNet  Google Scholar 

  20. Smith, P. A. New results and old problems in finite transformation groups. Bull. Amer. Math. Soc.66 (1960), 401–415.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, 251 Mercer Street, 10012, New York, N.Y.

    Sylvain E. Cappell & Julius L. Shaneson

  2. Department of Mathematics, Rutgers University, New Brunswick, N.J.

    Sylvain E. Cappell & Julius L. Shaneson

Authors
  1. Sylvain E. Cappell
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Julius L. Shaneson
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work supported by NSF Grant MCS-8002925.

This work supported by NSF Grant MCS 80-26053.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cappell, S.E., Shaneson, J.L. Class numbers and periodic smooth maps. Commentarii Mathematici Helvetici 58, 167–185 (1983). https://doi.org/10.1007/BF02564632

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02564632

Keywords

Search

Navigation