Skip to main content
Log in

The equivariant topological s-cobordism theorem

  • 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

  • [A] Anderson, D.R.: Torsion invariants and actions of finite groups. Mich. Math. J.29, 27–42 (1982)

    Google Scholar 

  • [AH] Anderson, D.R., Hsiang, W.-C.: The functorsK −i and pseudo-isotopies of polyhedra. Ann. Math105, 201–223 (1977)

    Google Scholar 

  • [AK] Araki, S., Kawakubo, K.: Equivariants-cobordism theorems (Preprint)

  • [Ba] Barden, D.: The Structure of Manifolds. Doctoral thesis. Cambridge University 1963

  • [BHS] Bass, H., Heller, A., Swan, R.: The Whitehead group of a polynomial extension. Publ. Inst. hautes Etud. Sci.22 (1964)

  • [Bo] Borsuk, K.: Sur l'élimination de phenomènes paradoxaux in topologie générale. Proc. Int. Congr. Math. vol. 1, pp. 197–208. Amsterdam, 1954

    Google Scholar 

  • [BH] Browder, W., Hsiang, W.-C.: Some problems on homotopy theory manifolds and transformation groups. Proc. Symp. Pure Math. vol. 32 part II, pp. 251–267, Am. Math. Soc., Providence, RI, 1978

    Google Scholar 

  • [BQ] Browder, W., Quinn, F.: A surgery theory forG-manifolds and stratified sets, Manifolds (Tokyo 1973). University Tokyo Press, Tokyo, 1975, pp. 27–36

    Google Scholar 

  • [Ca] Carter, D.: LowerK-theory of finite groups. Commun. Algebra8, 1927–1937 (1980)

    Google Scholar 

  • [C1] Chapman, T.A.: Cell-like mappings of Hilbert Cube manifolds: applications to simple homotopy theory. Bull. Am. Math. Soc.79, 1286–1291 (1973)

    Google Scholar 

  • [C2] Chapman, T.A.: Lectures on Hilbert Cube Manifolds. CBMS Regional Conf. Ser. in Math.28, Am. Math. Soc., Providence, RI, 1976

    Google Scholar 

  • [C3] Chapman, T.A.: Controlled Simple Homotopy Theory. (Lect. Notes Math. vol. 1009) Berlin Heidelberg New York: Springer 1983

    Google Scholar 

  • [C4] Chapman, T.A.: Controlled boundary and h-cobordism theorems. Trans. Am. Math. Soc.280, 73–95 (1983)

    Google Scholar 

  • [CF] Chapman, T.A., Ferry, S.: Approximating homotopy equivalences by homeomorphisms. Am. J. Math.101, 583–607 (1979)

    Google Scholar 

  • [Co] Cohen, M.M.: A Course in Simple Homotopy Theory. Berlin Heidelberg New York: Springer 173

  • [DR1] Dovermann, K.H., Rothenberg, M.: An equivariant surgery sequence and equivariant diffeomorphism and homeomorphism classification (announcement). Topology Symposium Siegen 1979. (Lect. Notes Math. vol. 788, pp. 257–280) Berlin Heidelberg New York: Springer 1980

    Google Scholar 

  • [DR2] Dovermann, K.H., Rothenberg, M.: An equivariant surgery sequence and equivariant diffeomorphism and homeomorphism classification (Preprint)

  • [F1] Ferry, S.: The homeomorphism group of a compact Hilbert cube manifold is an ANR. Ann. Math.106, 101–119 (1977)

    Google Scholar 

  • [F2] Ferry, S.: A Simple-homotopy approach to the finiteness obstruction, Shape Theory and Geometric Topology (Dubrovnik 1981). (Lect. Notes in Math. vol. 870, pp. 73–81) Berlin Heidelberg New York: Springer 1981

    Google Scholar 

  • [G] Giffen, C.: The generalized Smith Conjecture. Am. J. Math.88, 187–198 (1966)

    Google Scholar 

  • [H] Hauschild, H.: Äquivariante Whiteheadtorsion. Manuscr. Math.26, 63–82 (1978)

    Google Scholar 

  • [Il1] Illman, S.: Whitehead Torsion and group actions. Ann. Acad. Sci. Fenn. Ser. A.588, 1–44 (1974)

    Google Scholar 

  • [Il2] Illman, S.: Recognition of linear actions on spheres Trans. Am. Math. Soc.274, 445–478 (1982)

    Google Scholar 

  • [KS] Kahn, P.J., Steinberger, M.: Equivariant structure spaces (In preparation)

  • [KSi] Kirby, R.C., Siebenmann, L.C.: Foundational Essays on Topological Manifolds, Smoothings and Triangulations. Ann. Math. Stud., vol. 88, Princeton University Press, Princeton, NJ, 1977

    Google Scholar 

  • [LR] Lashof, R., Rothenberg, M.:G-smoothing theory. Proc. Symp. Pure Math. vol. 32, part I AMS, Providence, RI, 1978, pp. 211–266

    Google Scholar 

  • [Ma] Mazur, B.: Differential topology from the point of view of simple homotopy theory. Publ. Inst. Hautes Etud. Sci.15, 5–93 (1963)

    Google Scholar 

  • [Mi] Milnor, J.: Two complexes that are homeomorphic but combinatorially distinct. Ann. Math.74, 575–590 (1961)

    Google Scholar 

  • [Q1] Quinn, F.: Ends of Maps I. Ann. Math.110, 275–331 (1979)

    Google Scholar 

  • [Q2] Quinn, F.: Ends of Maps II. Invent. Math.68, 353–424 (1982)

    Google Scholar 

  • [Q3] Quinn, F.: Weakly stratified sets (Preprint)

  • [Ran] Ranicki, A.: Algebraic and geometric splittings of theK- andL-groups of polynomial extensions (Preprint)

  • [R] Rothenberg, M.: Torsion invariants and Finite transformation groups. Proc. Symp. Pure Math. 32, part I, AMS, Providence, RI, 1978, pp. 276–311

    Google Scholar 

  • [Si1] Siebenmann, L.C.: Obstructions to Finding a Boundary for an Open Manifold, Doctoral thesis, Princeton University 1965

  • [Si2] Siebenmann, L.C.: Infinite simple homotopy types. Indag. Math.32, 479–495 (1970)

    Google Scholar 

  • [Si3] Siebenmann, L.C.: Topological manifolds. Proc. Internat. Cong. Math., Nice, Sept. 1970, Gauthier-Villars, editeur, Paris 6e, 1971, vol. 2, pp. 133–163

    Google Scholar 

  • [Si4] Siebenmann, L.C.: Deformation of homeomorphisms on stratified sets. Comment. Math. Helv.47, 123–163 (1972)

    Google Scholar 

  • [SGH] Siebenmann, L.C., Guillou, L., Hähl, H.: Les voisanages ouverts réguliers: critères homotopiques d'existence. Ann. Sci. Ec. Norm. Su7, 431–461 (1974)

    Google Scholar 

  • [Sta] Stallings, J.: Notes on Polyhedral Topology. Tata Institute, 1968

  • [SW1] Steinberger, M., West, J.: Equivariant h-cobordisms and finiteness obstructions. Bull. Am. Math. Soc.12, 217–220 (1985)

    Google Scholar 

  • [SW2] Steinberger, M., West, J.: Approximation by equivariant homeomorphisms (revised version) (To appear in Trans Am. Math. Soc.)

  • [SW3] Steinberger, M., West, J.: Controlled finiteness is the obstruction to equivariant handle decomposition (Preprint)

  • [SW4] Steinberger, M., West, J.: Equivariant controlled simple homotopy theory (In preparation)

  • [SW5] Steinberger, M., West, J.: Equivariant Hilbert cube manifold theory (In preparation)

  • [Webb] Webb, D.: Equivariantly finite manifolds with no handle structure (Preprint)

  • [Wei] Weinberger, S.: Class numbers, the Novikov conjecture and transformation groups (Preprint)

  • [W] West, J.: Mapping Hilbert cube manifolds to ANR's: a solution of a conjecture of Borsuk. Ann. Math.106, 1–18 (1977)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Partially supported by the NSF and by the Graduate School of Northern Illinois University

Rights and permissions

Reprints and permissions

About this article

Cite this article

Steinberger, M. The equivariant topological s-cobordism theorem. Invent Math 91, 61–104 (1988). https://doi.org/10.1007/BF01404913

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01404913

Navigation