Duke Mathematical Journal

$K_2$ invariants of $3$-dimensional pseudoisotopies

Sławomir Kwasik and Reinhard Schultz
Source: Duke Math. J. Volume 78, Number 2 (1995), 359-371.
First Page: Show Hide
Primary Subjects: 19D50
Secondary Subjects: 57M60, 57N37
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077285751
Mathematical Reviews number (MathSciNet): MR1333505
Zentralblatt MATH identifier: 0866.57017
Digital Object Identifier: doi:10.1215/S0012-7094-95-07816-8

References

[ABK] P. L. Antonelli, D. Burghelea, and P. J. Kahn, The concordance-homotopy groups of geometric automorphism groups, Lecture Notes in Mathematics, vol. 215, Springer-Verlag, Berlin, 1971.
Mathematical Reviews (MathSciNet): MR50:11293
Zentralblatt MATH: 0222.57001
[B] H. Bass, $K$-theory and stable algebra, Inst. Hautes Études Sci. Publ. Math. (1964), no. 22, 5–60.
Mathematical Reviews (MathSciNet): MR30:4805
Zentralblatt MATH: 0248.18025
Digital Object Identifier: doi:10.1007/BF02684689
[BK] A. Bak and M. Kolster, The computation of odd-dimensional projective surgery groups of finite groups, Topology 21 (1982), no. 1, 35–63.
Mathematical Reviews (MathSciNet): MR82j:57032
Zentralblatt MATH: 0465.57016
Digital Object Identifier: doi:10.1016/0040-9383(82)90040-4
[Bon] F. Bonahon, Difféotopies des espaces lenticulaires, Topology 22 (1983), no. 3, 305–314.
Mathematical Reviews (MathSciNet): MR85d:57008
Zentralblatt MATH: 0526.57009
Digital Object Identifier: doi:10.1016/0040-9383(83)90016-2
[Bor] A. Borel, Stable real cohomology of arithmetic groups, Ann. Sci. École Norm. Sup. (4) 7 (1974), 235–272 (1975).
Mathematical Reviews (MathSciNet): MR52:8338
Zentralblatt MATH: 0316.57026
[BoS] A. Borel and J. P. Serre, Corners and arithmetic groups, Comment. Math. Helv. 48 (1973), 436–491.
Mathematical Reviews (MathSciNet): MR52:8337
Zentralblatt MATH: 0274.22011
Digital Object Identifier: doi:10.1007/BF02566134
[BPW] W. Browder, T. Petrie, and C. T. C. Wall, The classification of free actions of cyclic groups of odd order on homotopy spheres, Bull. Amer. Math. Soc. 77 (1971), 455–459.
Mathematical Reviews (MathSciNet): MR43:5547
Zentralblatt MATH: 0214.22601
Digital Object Identifier: doi:10.1090/S0002-9904-1971-12736-2
Project Euclid: euclid.bams/1183532832
[CS] S. Cappell and J. Shaneson, On four-dimensional $s$-cobordisms. II, Comment. Math. Helv. 64 (1989), no. 2, 338–347.
Mathematical Reviews (MathSciNet): MR90i:57011
Zentralblatt MATH: 0685.57011
Digital Object Identifier: doi:10.1007/BF02564679
[Ch] R. Charney, A note on excision in $K$-theory, Algebraic $K$-theory, number theory, geometry and analysis (Bielefeld, 1982), Lecture Notes in Math., vol. 1046, Springer, Berlin, 1984, pp. 47–54.
Mathematical Reviews (MathSciNet): MR85k:18015
Zentralblatt MATH: 0534.18006
Digital Object Identifier: doi:10.1007/BFb0072017
[DKS] K. Dennis, M. Keating, and M. Stein, Lower bounds for the order of $K\sb2(\bf ZG)$ and $\bf Wh\sb2(G)$, Math. Ann. 223 (1976), no. 2, 97–103.
Mathematical Reviews (MathSciNet): MR54:279
Zentralblatt MATH: 0342.18006
Digital Object Identifier: doi:10.1007/BF01360875
[DS] K Dennis and M. Stein, The functor $K\sb2$: a survey of computations and problems, Algebraic $K$-theory, II: “Classical” algebraic $K$-theory and connections with arithmetic (Proc. Conf., Seattle Res. Center, Battelle Memorial Inst., 1972), Springer, Berlin, 1973, 243–280. Lecture Notes in Math., Vol. 342.
Mathematical Reviews (MathSciNet): MR50:7292
Zentralblatt MATH: 0271.18011
[FJ] F. T. Farrell and L. Jones, Isomorphism conjectures in algebraic $K$-theory, J. Amer. Math. Soc. 6 (1993), no. 2, 249–297.
Mathematical Reviews (MathSciNet): MR93h:57032
Zentralblatt MATH: 0798.57018
Digital Object Identifier: doi:10.2307/2152801
[G] H. Garland, A finiteness theorem for $K\sb2$ of a number field, Ann. of Math. (2) 94 (1971), 534–548.
Mathematical Reviews (MathSciNet): MR45:6785
Zentralblatt MATH: 0247.12103
Digital Object Identifier: doi:10.2307/1970769
[GN] R. Geoghegan and A. Nicas, Parametrized Lefschetz-Nielsen fixed point theory and Hochschild homology traces, Amer. J. Math. 116 (1994), no. 2, 397–446.
Mathematical Reviews (MathSciNet): MR95a:55005
Zentralblatt MATH: 0812.55001
Digital Object Identifier: doi:10.2307/2374935
[H] A. Hatcher, Concordance spaces, higher simple-homotopy theory, and applications, Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976), Part 1, Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc., Providence, R.I., 1978, pp. 3–21.
Mathematical Reviews (MathSciNet): MR80f:57014
Zentralblatt MATH: 0406.57031
[HW] A. Hatcher and J. Wagoner, Pseudo-isotopies of compact manifolds, Astérisque, vol. 6, Société Mathématique de France, Paris, 1973.
Mathematical Reviews (MathSciNet): MR50:5821
Zentralblatt MATH: 0274.57011
[HR] C. Hodgson and J. H. Rubinstein, Involutions and isotopies of lens spaces, Knot theory and manifolds (Vancouver, B.C., 1983), Lecture Notes in Math., vol. 1144, Springer, Berlin, 1985, pp. 60–96.
Mathematical Reviews (MathSciNet): MR87h:57028
Zentralblatt MATH: 0605.57022
Digital Object Identifier: doi:10.1007/BFb0075012
[HsS] W.-C. Hsiang and R. Sharpe, Parametrized surgery and isotopy, Pacific J. Math. 67 (1976), no. 2, 401–459.
Mathematical Reviews (MathSciNet): MR58:13091
Zentralblatt MATH: 0348.57015
Project Euclid: euclid.pjm/1102817501
[I1] K. Igusa, What happens to Hatcher and Wagoner's formulas for $\pi \sb0C(M)$ when the first Postnikov invariant of $M$ is nontrivial? Algebraic $K$-theory, number theory, geometry and analysis (Bielefeld, 1982), Lecture Notes in Math., vol. 1046, Springer, Berlin, 1984, pp. 104–172.
Mathematical Reviews (MathSciNet): MR86a:57026
Zentralblatt MATH: 0546.57015
Digital Object Identifier: doi:10.1007/BFb0072020
[I2] K. Igusa, The stability theorem for smooth pseudoisotopies, $K$-Theory 2 (1988), no. 1-2, vi+355.
Mathematical Reviews (MathSciNet): MR90d:57035
Zentralblatt MATH: 0691.57011
Digital Object Identifier: doi:10.1007/BF00533643
[I3] K. Igusa, Unstable pseudo-isotopy, 1990, Abstracts of Topology Conference, Oberwolfach.
[J] B. Jahren, On the rational $K$-theory of group rings of finite groups, preprint, University of Oslo, 1994.
[Ku] A. Kuku, Some finiteness results in the higher $K$-theory of orders and group-rings, Topology Appl. 25 (1987), no. 2, 185–191.
Mathematical Reviews (MathSciNet): MR88m:11100
Zentralblatt MATH: 0608.18005
Digital Object Identifier: doi:10.1016/0166-8641(87)90013-7
[Kw] S. Kwasik, Low-dimensional concordances, Whitney towers and isotopies, Math. Proc. Cambridge Philos. Soc. 102 (1987), no. 1, 103–119.
Mathematical Reviews (MathSciNet): MR88d:57016
Zentralblatt MATH: 0642.57010
Digital Object Identifier: doi:10.1017/S0305004100067098
[KwS1] S. Kwasik and R. Schultz, Unitary nilpotent groups and the stability of pseudoisotopies, Duke Math. J. 71 (1993), no. 3, 871–887.
Mathematical Reviews (MathSciNet): MR94m:57047
Zentralblatt MATH: 0804.57009
Digital Object Identifier: doi:10.1215/S0012-7094-93-07133-5
Project Euclid: euclid.dmj/1077290283
[KwS2] S. Kwasik and R. Schultz, On $s$-cobordisms of metacyclic prism manifolds, Invent. Math. 97 (1989), no. 3, 523–552.
Mathematical Reviews (MathSciNet): MR90e:57063
Zentralblatt MATH: 0688.57019
Digital Object Identifier: doi:10.1007/BF01388889
[KwS3] S. Kwasik and R. Schultz, Visible surgery, $4$-dimensional $s$-cobordisms and related questions in geometric topology, to appear in $K$-Theory.
Mathematical Reviews (MathSciNet): MR1351942
Digital Object Identifier: doi:10.1007/BF00961468
[McR] D. McCullough and J. H. Rubinstein, The generalized Smale conjecture for $3$-manifolds with genus $2$ one-sided Heegaard splittings, to appear.
[NS] A. Nicas and C. Stark, Higher Whitehead groups of certain bundles over Seifert manifolds, Proc. Amer. Math. Soc. 91 (1984), no. 1, 1–5.
Mathematical Reviews (MathSciNet): MR85k:18018a
Zentralblatt MATH: 0565.57012
Digital Object Identifier: doi:10.2307/2045256
[O1] R. Oliver, Lower bounds for $K\sp \rm top\sb 2(\hat\bf Z\sb p\pi)$ and $K\sb 2(\bf Z\pi)$, J. Algebra 94 (1985), no. 2, 425–487.
Mathematical Reviews (MathSciNet): MR87a:18016
Zentralblatt MATH: 0595.18004
Digital Object Identifier: doi:10.1016/0021-8693(85)90195-4
[O2] R. Oliver, $K\sb 2$ of $p$-adic group rings of abelian $p$-groups, Math. Z. 195 (1987), no. 4, 505–558.
Mathematical Reviews (MathSciNet): MR88k:18015
Zentralblatt MATH: 0625.18005
Digital Object Identifier: doi:10.1007/BF01166703
[O3] R. Oliver, $SK\sb 1$ of finite group rings. V, Comment. Math. Helv. 62 (1987), no. 3, 465–509.
Mathematical Reviews (MathSciNet): MR89d:18004
Zentralblatt MATH: 0627.16019
Digital Object Identifier: doi:10.1007/BF02564457
[O4] R. Oliver, Whitehead groups of finite groups, London Mathematical Society Lecture Note Series, vol. 132, Cambridge University Press, Cambridge, 1988.
Mathematical Reviews (MathSciNet): MR89h:18014
Zentralblatt MATH: 0636.18001
[Q1] D. Quillen, On the cohomology and $K$-theory of the general linear groups over a finite field, Ann. of Math. (2) 96 (1972), 552–586.
Mathematical Reviews (MathSciNet): MR47:3565
Zentralblatt MATH: 0249.18022
Digital Object Identifier: doi:10.2307/1970825
[Q2] D. Quillen, Higher $K$-theory for categories with exact sequences, New developments in topology (Proc. Sympos. Algebraic Topology, Oxford, 1972), Cambridge Univ. Press, London, 1974, 95–103. London Math. Soc. Lecture Note Ser., No. 11.
Mathematical Reviews (MathSciNet): MR49:384
Zentralblatt MATH: 0276.18013
[Sch] R. Schultz, Homotopy decompositions of equivariant function spaces. I, Math. Z. 131 (1973), 49–75.
Mathematical Reviews (MathSciNet): MR53:11636
Zentralblatt MATH: 0244.55020
Digital Object Identifier: doi:10.1007/BF01213825
[Ss] A. Suslin, Stability in algebraic $K$-theory, Algebraic $K$-theory, Part I (Oberwolfach, 1980), Lecture Notes in Math., vol. 966, Springer, Berlin, 1982, pp. 304–333.
Mathematical Reviews (MathSciNet): MR85d:18011
Zentralblatt MATH: 0498.18008
[T] G. Triantafillou, Diffeomorphisms of manifolds with finite fundamental group, Bull. Amer. Math. Soc. (N.S.) 31 (1994), no. 1, 50–53.
Mathematical Reviews (MathSciNet): MR94j:57029
Zentralblatt MATH: 0817.57027
Digital Object Identifier: doi:10.1090/S0273-0979-1994-00496-3
[Wa] F. Waldhausen, Algebraic $K$-theory of generalized free products, Ann. of Math. (2) 108 (1970), 135–256.
[W1] C. T. C. Wall, Classification of Hermitian Forms. VI. Group rings, Ann. of Math. (2) 103 (1976), no. 1, 1–80.
Mathematical Reviews (MathSciNet): MR55:5720
Zentralblatt MATH: 0328.18006
Digital Object Identifier: doi:10.2307/1971019
[We] C. Weibel, Mayer-Vietoris sequences and module structures on $NK\sb\ast$, Algebraic $K$-theory, Evanston 1980 (Proc. Conf., Northwestern Univ., Evanston, Ill., 1980), Lecture Notes in Math., vol. 854, Springer, Berlin, 1981, pp. 466–493.
Mathematical Reviews (MathSciNet): MR82k:18010
Zentralblatt MATH: 0487.18012

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