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Summary: Background material and basic results

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1443)

Keywords

  • Surgery Theory
  • Equivariant Homotopy
  • Twisted Product
  • Obstruction Group
  • Surgery Obstruction

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. G. A. Anderson, “Surgery with Coefficients,” Lecture Notes in Mathematics Vol. 591, Springer, Berlin-Heidelberg-New York, 1977.

    MATH  Google Scholar 

  2. G. Bredon, “Introduction to Compact Transformation Groups,” Pure and Applied Mathematics Vol. 46, Academic Press, New York, 1972.

    MATH  Google Scholar 

  3. W. Browder, Manifolds and homotopy theory, in “Manifolds—Amsterdam 1970 (Proc. NUFFIC Summer School, Amsterdam, Neth., 1970),” Lecture Notes in Mathematics Vol. 197, Springer, Berlin-Heidelberg-New York, 1971, pp. 17–35.

    CrossRef  Google Scholar 

  4. W. Browder and F. Quinn, A surgery theory for G-manifolds and stratified sets, in “Manifolds-Tokyo, 1973,” (Conf. Proc. Univ of Tokyo, 1973), University of Tokyo Press, Tokyo, 1975, pp. 27–36.

    Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. T. tom Dieck, “Transformation Groups,” de Gruyter Studies in Mathematics Vol. 8, W. de Gruyter, Berlin and New York, 1987.

    CrossRef  MATH  Google Scholar 

  7. K. H. Dovermann and T. Petrie, G-Surgery II, Memoirs Amer. Math. Soc. 37 (1982), No. 260.

    Google Scholar 

  8. _____, An induction theorem for equivariant surgery (G-Surgery III), Amer. J. Math. 105 (1983), 1369–1403.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. K. H. Dovermann and M. Rothenberg, Equivariant Surgery and Classification of Finite Group Actions on Manifolds, Memoirs Amer. Math. Soc. 71 (1988), No. 379.

    Google Scholar 

  10. _____, An algebraic approach to the generalized Whitehead group, in “Transformation Groups (Proceedings, Poznań, 1985),” Lecture Notes in Mathematics Vol. 1217, Springer, Berlin-Heidelberg-New York, 1986, pp. 92–114.

    Google Scholar 

  11. S. Illman, Equivariant Whitehead torsion and actions of compact Lie groups, in “Group Actions on Manifolds (Conference Proceedings, University of Colorado, 1983),” Contemp. Math. Vol. 36, American Mathematical Society, 1985, pp. 91–106.

    Google Scholar 

  12. R. C. Kirby and L. C. Siebenmann, “Foundational Essays on Topological Manifolds, Smoothings, and Triangulations,” Annals of Mathematics Studies Vol. 88, Princeton University Press, Princeton, 1977.

    CrossRef  MATH  Google Scholar 

  13. C. Latour, Chirurgie non simplement connexe (d’après C. T. C. Wall), in “Séminaire Bourbaki Vol. 1970–1971,” Lecture Notes in Mathematics Vol. 244, Exposé 397, Springer, Berlin-Heidelberg-New York, 1971, pp. 289–322.

    CrossRef  Google Scholar 

  14. J. A. Lees, The surgery obstruction groups of C. T. C. Wall, Advances in Math. 11 (1973), 113–156.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. W. Lellmann, Orbiträume von G-Mannigfaltigkeiten und stratifizierte Mengen, Diplomarbeit, Universität Bonn, 1975.

    Google Scholar 

  16. W. Lück and I. Madsen, Equivariant L-theory I, Aarhus Univ. Preprint Series (1987/1988), No. 8; [same title] II, Aarhus Univ. Preprint Series (1987/1988), No. 16.

    Google Scholar 

  17. J. Milnor and J. Stasheff, “Characteristic Classes,” Annals of Mathematics Studies Vol. 76, Princeton University Press, Princeton, 1974.

    CrossRef  MATH  Google Scholar 

  18. A. Nicas, Induction theorems for groups of homotopy manifold structures, Memoirs Amer. Math. Soc. 39 (1982). No. 267.

    Google Scholar 

  19. A. A. Ranicki, The algebraic theory of surgery I: Foundations, Proc. London Math. Soc. 3:40 (1980), 87–192.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. _____, The algebraic theory of surgery II: Applications to topology, Proc. London Math. Soc. 3:40 (1980), 193–283.

    CrossRef  MathSciNet  MATH  Google Scholar 

  21. R. Schultz, An infinite exact sequence in equivariant surgery, Mathematisches Forschungsinstitut Oberwolfach Tagungsbericht 14/1985 (Surgery and L-theory), 4–5.

    Google Scholar 

  22. E. H. Spanier, “Algebraic Topology,” McGraw-Hill, New York, 1967.

    MATH  Google Scholar 

  23. C.T.C. Wall, “Surgery on Compact Manifolds,” London Math. Soc. Monographs Vol. 1, Academic Press, London and New York, 1970.

    MATH  Google Scholar 

  24. M. Yan, Periodicity in equivariant surgery and applications, Ph. D. Thesis, University of Chicago, in preparation.

    Google Scholar 

  25. T. Yoshida, Surgery obstructions of twisted products, J. Math. Okayama Univ. 24 (1982), 73–97.

    MATH  Google Scholar 

Addendum: Additional references related to [Wa]

  1. Th. Bröcker and K. Jänich, “Introduction to Differential Topology,” (Transl. by C. B. and M. J. Thomas), Cambridge University Press, Cambridge, U. K., and New York, 1982.

    Google Scholar 

  2. W. Browder, “Surgery on Simply Connected Manifolds,” Ergeb. der Math. (2) 65, Springer, New York, 1972.

    CrossRef  MATH  Google Scholar 

  3. M. Cohen, “A Course in Simple Homotopy Theory,” Graduate Texts in Mathematics Vol. 10, Springer, Berlin-Heidelberg-New York, 1973.

    CrossRef  MATH  Google Scholar 

  4. A. Haefliger and V. Poenaru, La classification des immersions combinatories, I. H. E. S. Publ. Math. 23 (1964), 75–91.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. M. W. Hirsch, Immersions of differentiable manifolds, Trans. Amer. Math. Soc. 93 (1959), 242–276.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. _____, “Differential Topology,” Graduate Texts in Mathematics Vol. 33, Springer, Berlin-Heidelberg-New York, 1976.

    MATH  Google Scholar 

  7. J. F. P. Hudson, “Piecewise Linear Topology,” W. A. Benjamin, New York, 1969.

    MATH  Google Scholar 

  8. M. Kervaire, Le théorème de Barden-Mazur-Stallings, Comment. Math. Helv. 40 (1965), 31–42.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. J. Milnor, “Lectures on the h-cobordism Theorem,” Princeton Mathematical Notes No. 1, Princeton University Press, Princeton, N. J., 1965.

    CrossRef  MATH  Google Scholar 

  10. J. R. Munkres, “Elementary Differential Topology (Revised Edition),” Annals of Mathematics Studies Vol. 54, Princeton University Press, Princeton, N. J., 1966.

    MATH  Google Scholar 

  11. A. V. Phillips, Submersions of open manifolds, Topology 6 (1967), 171–206.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. C. P. Rourke and B. J. Sanderson, “Introduction to Piecewise Linear Topology,” Ergebnisse der Math. Bd. 69, Springer, Berlin-Heidelberg-New York, 1972.

    CrossRef  MATH  Google Scholar 

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© 1990 Springer-Verlag

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Dovermann, K.H., Schultz, R. (1990). Summary: Background material and basic results. In: Equivariant Surgery Theories and Their Periodicity Properties. Lecture Notes in Mathematics, vol 1443. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092355

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  • DOI: https://doi.org/10.1007/BFb0092355

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