On 3-manifolds admitting orientation-reversing involutions

Akio KAWAUCHI

doi:10.2969/jmsj/03340571

Akio KAWAUCHI

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JOURNAL FREE ACCESS

1981 Volume 33 Issue 4 Pages 571-589

DOI https://doi.org/10.2969/jmsj/03340571

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Published: 1981 Received: December 19, 1979 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) D. Barden, Simply connected 5-manifolds, Ann. of Math., 82 (1965), 365-385.
2) J. S. Birman, Orientation-reversing involutions on 3-manifolds (unpublished, 1978).
3) A. Borel et al., Seminar on Transformation Groups, Ann. of Math. Studies 46, Princeton University Press.
4) G. Bredon, The cohomology ring structure of a fixed set, Ann. of Math., 80 (1964), 524-537.
5) W. Browder, Remark on the Poincaré duality theorem, Proc. Amer. Math. Soc., 13 (1962), 927-930.
6) D. Galewski and R. Stern, Orientation-reversing involutions on homology 3-spheres, Math. Proc. Cambridge Philos. Soc., 85 (1979), 449-451.
7) H. Hopf, Fundamentalgruppe und zweite Bettische Gruppe, Comment. Math. Helvet., 14 (1941-1942), 257-309.
8) W. C. Hsiang and P. Pao, The homology 3-spheres with involutions, Proc. Amer. Math. Soc., 75 (1979), 308-310.
9) W. Y. Hsiang, Cohomology Theory of Topological Transformation Groups, Springer-Verlag, 1975.
10) S. J. Kaplan, Constructing framed 4-manifolds with given almost framed boundaries, Trans. Amer. Math. Soc., 254 (1979), 237-263.
11) A. Kawauchi, Three dimensional homology handles and circles, Osaka J. Math., 12 (1975), 565-581.
12) A. Kawauchi, H-cobordism, I; The groups among three dimensional homology handles, Osaka J. Math., 13 (1976), 567-590.
13) A. Kawauchi, On n-manifolds whose punctured manifolds are imbeddable in (n+1)-spheres and spherical manifolds, Hiroshima Math. J., 9 (1979), 47-57.
14) A. Kawauchi, Vanishing of the Rochlin invariants of some Z₂-homology 3-spheres, Proc. Amer. Math. Soc., 79 (1980), 303-307.
15) K. W. Kwun, Scarcity of orientation-reversing PL involutions of lens spaces, Michigan Math. J., 17 (1970), 355-358.
16) G. Lusztig, J. Milnor and F. P. Peterson, Semi-characteristics and cobordism, Topology, 8 (1969), 357-359.
17) J. W. Milnor, Spin structures on manifolds, L'Enseignement Math., 9 (1963), 198-203.
18) R. Robertello, An invariant of knot cobordism, Comm. Pure Appl. Math., 18(1965), 543-555.

Right : [1] D. Barden, Simply connected 5-manifolds, Ann. of Math., 82 (1965), 365-385.
[2] J. S. Birman, Orientation-reversing involutions on 3-manifolds (unpublished, 1978).
[3] A. Borel et al., Seminar on Transformation Groups, Ann. of Math. Studies 46, Princeton University Press.
[4] G. Bredon, The cohomology ring structure of a fixed set, Ann. of Math., 80 (1964), 524-537.
[5] W. Browder, Remark on the Poincaré duality theorem, Proc. Amer. Math. Soc., 13 (1962), 927-930.
[6] D. Galewski and R. Stern, Orientation-reversing involutions on homology 3-spheres, Math. Proc. Cambridge Philos. Soc., 85 (1979), 449-451.
[7] H. Hopf, Fundamentalgruppe und zweite Bettische Gruppe, Comment. Math. Helvet., 14 (1941-1942), 257-309.
[8] W. C. Hsiang and P. Pao, The homology 3-spheres with involutions, Proc. Amer. Math. Soc., 75 (1979), 308-310.
[9] W. Y. Hsiang, Cohomology Theory of Topological Transformation Groups, Springer-Verlag, 1975.
[10] S. J. Kaplan, Constructing framed 4-manifolds with given almost framed boundaries, Trans. Amer. Math. Soc., 254 (1979), 237-263.
[11] A. Kawauchi, Three dimensional homology handles and circles, Osaka J. Math., 12 (1975), 565-581.
[12] A. Kawauchi, H-cobordism, I; The groups among three dimensional homology handles, Osaka J. Math., 13 (1976), 567-590.
[13] A. Kawauchi, On n-manifolds whose punctured manifolds are imbeddable in (n+1)-spheres and spherical manifolds, Hiroshima Math. J., 9 (1979), 47-57.
[14] A. Kawauchi, Vanishing of the Rochlin invariants of some Z₂-homology 3-spheres, Proc. Amer. Math. Soc., 79 (1980), 303-307.
[15] K. W. Kwun, Scarcity of orientation-reversing PL involutions of lens spaces, Michigan Math. J., 17 (1970), 355-358.
[16] G. Lusztig, J. Milnor and F. P. Peterson, Semi-characteristics and cobordism, Topology, 8 (1969), 357-359.
[17] J. W. Milnor, Spin structures on manifolds, L'Enseignement Math., 9 (1963), 198-203.
[18] R. Robertello, An invariant of knot cobordism, Comm. Pure Appl. Math., 18(1965), 543-555.

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