Book Review
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MathSciNet review:
1568038
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Book Information:
Author:
K. H. Dovermann and Reinhard Schultz
Title:
Equivariant surgery theories and their periodicity properties
Additional book information:
Lecture Notes in Mathematics, vol.~1443, Springer-Verlag, New York, 1990, 225 pp. US$24.00. ISBN 3-540-53042-8.
Douglas R. Anderson and Hans J. Munkholm, Boundedly controlled topology, Lecture Notes in Mathematics, vol. 1323, Springer-Verlag, Berlin, 1988. Foundations of algebraic topology and simple homotopy theory. MR 953961, DOI 10.1007/BFb0079806
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
Sylvain E. Cappell and Julius L. Shaneson, Nonlinear similarity, Ann. of Math. (2) 113 (1981), no. 2, 315–355. MR 607895, DOI 10.2307/2006986
Sylvain Cappell and Shmuel Weinberger, A geometric interpretation of Siebenmann’s periodicity phenomenon, Geometry and topology (Athens, Ga., 1985) Lecture Notes in Pure and Appl. Math., vol. 105, Dekker, New York, 1987, pp. 47–52. MR 873283
[DM] J. Davis and J. Milgram, A survey of the spherical space form problem, Mathematical Surveys, vol. 2, Harwood, New York, 1985.
Karl Heinz Dovermann and Ted Petrie, $G$ surgery. II, Mem. Amer. Math. Soc. 37 (1982), no. 260, xxiii+118. MR 652862, DOI 10.1090/memo/0260
Karl Heinz Dovermann and Melvin Rothenberg, Equivariant surgery and classifications of finite group actions on manifolds, Mem. Amer. Math. Soc. 71 (1988), no. 379, viii+117. MR 920965, DOI 10.1090/memo/0379
F. T. Farrell and L. E. Jones, A topological analogue of Mostow’s rigidity theorem, J. Amer. Math. Soc. 2 (1989), no. 2, 257–370. MR 973309, DOI 10.1090/S0894-0347-1989-0973309-4
[FP] S. Ferry and E. Pederson, Epsilon surgery theory, Binghamton preprint (to appear).
Karsten Grove, Peter Petersen V, and Jyh Yang Wu, Geometric finiteness theorems via controlled topology, Invent. Math. 99 (1990), no. 1, 205–213. MR 1029396, DOI 10.1007/BF01234418
M. A. Kervaire, Lectures on the theorem of Browder and Novikov and Siebenmann’s thesis, Tata Institute of Fundamental Research Lectures on Mathematics, No. 46, Tata Institute of Fundamental Research, Bombay, 1969. Notes by K. Varadarajan. MR 0339227
Michel A. Kervaire and John W. Milnor, Groups of homotopy spheres. I, Ann. of Math. (2) 77 (1963), 504–537. MR 148075, DOI 10.1090/S0273-0979-2015-01504-1
Wolfgang Lück and Ib Madsen, Equivariant $L$-theory. I, Math. Z. 203 (1990), no. 3, 503–526. MR 1038715, DOI 10.1007/BF02570753
I. Madsen, C. B. Thomas, and C. T. C. Wall, The topological spherical space form problem. II. Existence of free actions, Topology 15 (1976), no. 4, 375–382. MR 426003, DOI 10.1016/0040-9383(76)90031-8
John Milnor, A procedure for killing homotopy groups of differentiable manifolds. , Proc. Sympos. Pure Math., Vol. III, American Mathematical Society, Providence, R.I., 1961, pp. 39–55. MR 0130696
John Milnor, Lectures on the $h$-cobordism theorem, Princeton University Press, Princeton, N.J., 1965. Notes by L. Siebenmann and J. Sondow. MR 0190942
John W. Morgan and Dennis P. Sullivan, The transversality characteristic class and linking cycles in surgery theory, Ann. of Math. (2) 99 (1974), 463–544. MR 350748, DOI 10.2307/1971060
Frank Quinn, Resolutions of homology manifolds, and the topological characterization of manifolds, Invent. Math. 72 (1983), no. 2, 267–284. MR 700771, DOI 10.1007/BF01389323
[Su1] D. Sullivan, Triangulating homotopy equivalences, Princeton Ph.D. thesis, 1966.
C. T. C. Wall, Surgery on compact manifolds, London Mathematical Society Monographs, No. 1, Academic Press, London-New York, 1970. MR 0431216
Shmuel Weinberger, Aspects of the Novikov conjecture, Geometric and topological invariants of elliptic operators (Brunswick, ME, 1988) Contemp. Math., vol. 105, Amer. Math. Soc., Providence, RI, 1990, pp. 281–297. MR 1047285, DOI 10.1090/conm/105/1047285
[WY] S. Weinberger and M. Yan, Products in stratified surgery and periodicity, preprint.
Tomoyoshi Yoshida, Surgery obstruction of twisted products, Math. J. Okayama Univ. 24 (1982), no. 1, 73–97. MR 660056
- [AM]
- D. Anderson and H. Munkholm, Boundedly controlled topology, Lecture Notes in Math., vol. 1323, Springer, New York, 1988. MR 953961 (89h:57029)
- [BQ]
- W. Browder and F. Quinn, A surgery theory for G-manifolds and stratified sets, Manifolds, Tokyo, 1973, Univ. of Tokyo Press, 1975, pp. 27-36. MR 0375348 (51:11543)
- [CS]
- S. Cappell and J. Shaneson, Nonlinear similarity, Ann. of Math. (2) 113 (1981), 311-351. MR 607895 (83h:57060)
- [CW]
- S. Cappell and S. Weinberger, A geometric interpretation of Siebenmann's periodicity phenomenon, Proc. 1986 Georgia Topology Conference (McCrory and Shiffrin, eds.), Marcel Dekker Inc., New York and Basel, pp. 47-52. MR 873283 (88f:57040)
- [DM]
- J. Davis and J. Milgram, A survey of the spherical space form problem, Mathematical Surveys, vol. 2, Harwood, New York, 1985.
- [DoP]
- K. H. Dovermann and T. Petrie, G surgery. II, Mem. Amer. Math. Soc., vol. 37, Amer. Math. Soc., Providence, RI, 1982. MR 652862 (84c:57025)
- [DoR]
- K. H. Dovermann and M. Rothenberg, Equivariant surgery and classification of finite group actions on manifolds, Mem. Amer. Math. Soc., vol. 71, Amer. Math. Soc., Providence, RI, 1988. MR 920965 (89h:57032)
- [FJ]
- F. T. Farrell and L. Jones, A topological analogue of Mostow's rigidity theorem, J. Amer. Math. Soc. 2 (1989), 257-370. MR 973309 (90h:57023a)
- [FP]
- S. Ferry and E. Pederson, Epsilon surgery theory, Binghamton preprint (to appear).
- [GPW]
- K. Grove, P. Peterson and J. Y. Wu, Geometric finiteness theorems and controlled topology, Invent. Math. 99 (1990), 205-214. MR 1029396 (90k:53075)
- [Ke]
- M. Kervaire, Lectures on the theorems of Browder and Novikov and Siebenmann's thesis, Tata Institute of Fundamental Res., 1969. MR 0339227 (49:3989)
- [KM]
- M. Kervaire and J. Milnor, Groups of homotopy spheres, Ann. of Math. (2) 77 (1963), 504-537. MR 0148075 (26:5584)
- [LM]
- W. Luck and I. Madsen, Equivariant L-theory. I, II, Math. Z. 203 (1990), 503-526; 204 (1990), 253-268. MR 1038715 (91d:57022)
- [MTW]
- I. Madsen, C. B. Thomas, and C. T. C. Wall, The topological spherical spaceform problem. II, Topology 15 (1976), 375-382. MR 0426003 (54:13952)
- [Mi1]
- J. Milnor, A procedure for killing the homotopy groups of a manifold, Proc. Sympos. Pure Math., vol. 3, Amer. Math. Soc., Providence, RI, 1961, pp. 39-55. MR 0130696 (24:A556)
- [Mi2]
- J. Milnor, Lectures on the h-cobordism theorem, Princeton Univ. Press, Princeton, NJ, 1965. MR 0190942 (32:8352)
- [MoS]
- J. Morgan and D. Sullivan, The transversality characteristic class and linking cycles in surgery theory, Ann. of Math. 99 (1974), 384-463. MR 0350748 (50:3240)
- [Q]
- F. Quinn, Resolution of homology manifolds, Invent. Math. 72 (1983), 267-284; Corrigendum 85 (1986), 653. MR 700771 (85b:57023)
- [Su1]
- D. Sullivan, Triangulating homotopy equivalences, Princeton Ph.D. thesis, 1966.
- [Wa]
- C. T. C. Wall, Surgery on compact manifolds, Academic Press, New York, 1971. MR 0431216 (55:4217)
- [Wei]
- S. Weinberger, Aspects of the Novikov conjecture in geometric invariants of elliptic operators, Contemp. Math. 105 (1990), 281-297. MR 1047285 (91a:57020)
- [WY]
- S. Weinberger and M. Yan, Products in stratified surgery and periodicity, preprint.
- [YO]
- T. Yoshida, Surgery obstructions of twisted products, J. Math. Okayama Univ. 24 (1982), 73-97. MR 660056 (83k:57027)
Review Information:
Reviewer:
Mel Rothenberg
Journal:
Bull. Amer. Math. Soc.
28 (1993), 375-382
DOI:
https://doi.org/10.1090/S0273-0979-1993-00368-9