Homotopically stratified sets
Author:
Frank Quinn
Journal:
J. Amer. Math. Soc. 1 (1988), 441-499
MSC:
Primary 57N37; Secondary 57N80, 57R80, 57S17
DOI:
https://doi.org/10.1090/S0894-0347-1988-0928266-2
MathSciNet review:
928266
Full-text PDF Free Access
References | Similar Articles | Additional Information
- Ethan Akin, Manifold phenomena in the theory of polyhedra, Trans. Amer. Math. Soc. 143 (1969), 413–473. MR 253329, DOI https://doi.org/10.1090/S0002-9947-1969-0253329-1
- Douglas R. Anderson and W. C. Hsiang, The functors $K_{-i}$ and pseudo-isotopies of polyhedra, Ann. of Math. (2) 105 (1977), no. 2, 201–223. MR 440573, DOI https://doi.org/10.2307/1970997
- Douglas R. Anderson and Wu Chung Hsiang, Extending combinatorial piecewise linear structures on stratified spaces. II, Trans. Amer. Math. Soc. 260 (1980), no. 1, 223–253. MR 570787, DOI https://doi.org/10.1090/S0002-9947-1980-0570787-8
- William Browder and Frank Quinn, A surgery theory for $G$-manifolds and stratified sets, Manifolds—Tokyo 1973 (Proc. Internat. Conf., Tokyo, 1973) Univ. Tokyo Press, Tokyo, 1975, pp. 27–36. MR 0375348
- David W. Carter, Lower $K$-theory of finite groups, Comm. Algebra 8 (1980), no. 20, 1927–1937. MR 590500, DOI https://doi.org/10.1080/00927878008822554
- T. A. Chapman, Lectures on Hilbert cube manifolds, American Mathematical Society, Providence, R. I., 1976. Expository lectures from the CBMS Regional Conference held at Guilford College, October 11-15, 1975; Regional Conference Series in Mathematics, No. 28. MR 0423357
- Marshall M. Cohen, A course in simple-homotopy theory, Springer-Verlag, New York-Berlin, 1973. Graduate Texts in Mathematics, Vol. 10. MR 0362320
- Edward Fadell, Generalized normal bundles for locally-flat imbeddings, Trans. Amer. Math. Soc. 114 (1965), 488–513. MR 179795, DOI https://doi.org/10.1090/S0002-9947-1965-0179795-4
- F. T. Farrell and W. C. Hsiang, The Whitehead group of poly-(finite or cyclic) groups, J. London Math. Soc. (2) 24 (1981), no. 2, 308–324. MR 631942, DOI https://doi.org/10.1112/jlms/s2-24.2.308
- Steve Ferry, A simple-homotopy approach to the finiteness obstruction, Shape theory and geometric topology (Dubrovnik, 1981) Lecture Notes in Math., vol. 870, Springer, Berlin-New York, 1981, pp. 73–81. MR 643523
- Michael H. Freedman and Frank Quinn, Topology of 4-manifolds, Princeton Mathematical Series, vol. 39, Princeton University Press, Princeton, NJ, 1990. MR 1201584
- W. C. Hsiang and William Pardon, When are topologically equivalent orthogonal transformations linearly equivalent?, Invent. Math. 68 (1982), no. 2, 275–316. MR 666164, DOI https://doi.org/10.1007/BF01394060
- Frank Quinn, Ends of maps. I, Ann. of Math. (2) 110 (1979), no. 2, 275–331. MR 549490, DOI https://doi.org/10.2307/1971262
- Frank Quinn, Finite nilpotent group actions on finite complexes, Geometric applications of homotopy theory (Proc. Conf., Evanston, Ill., 1977), I, Lecture Notes in Math., vol. 657, Springer, Berlin, 1978, pp. 375–407. MR 513560
- Frank Quinn, Intrinsic skeleta and intersection homology of weakly stratified sets, Geometry and topology (Athens, Ga., 1985) Lecture Notes in Pure and Appl. Math., vol. 105, Dekker, New York, 1987, pp. 233–249. MR 873296
- Frank Quinn, Algebraic $K$-theory of poly-(finite or cyclic) groups, Bull. Amer. Math. Soc. (N.S.) 12 (1985), no. 2, 221–226. MR 776473, DOI https://doi.org/10.1090/S0273-0979-1985-15353-4
- L. C. Siebenmann, Deformation of homeomorphisms on stratified sets. I, II, Comment. Math. Helv. 47 (1972), 123–136; ibid. 47 (1972), 137–163. MR 319207, DOI https://doi.org/10.1007/BF02566793
- Mark Steinberger, The equivariant topological $s$-cobordism theorem, Invent. Math. 91 (1988), no. 1, 61–104. MR 918237, DOI https://doi.org/10.1007/BF01404913
- Mark Steinberger and James West, Equivariant $h$-cobordisms and finiteness obstructions, Bull. Amer. Math. Soc. (N.S.) 12 (1985), no. 2, 217–220. MR 776472, DOI https://doi.org/10.1090/S0273-0979-1985-15351-0 ---, Controlled finiteness is the obstruction to equivariant handle decomposition (preprint).
- R. Thom, Ensembles et morphismes stratifiés, Bull. Amer. Math. Soc. 75 (1969), 240–284 (French). MR 239613, DOI https://doi.org/10.1090/S0002-9904-1969-12138-5
- Andrei Verona, Stratified mappings—structure and triangulability, Lecture Notes in Mathematics, vol. 1102, Springer-Verlag, Berlin, 1984. MR 771120
- C. T. C. Wall, Finiteness conditions for ${\rm CW}$-complexes, Ann. of Math. (2) 81 (1965), 56–69. MR 171284, DOI https://doi.org/10.2307/1970382
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© Copyright 1988
American Mathematical Society