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A remark on the exotic free actions in dimension 4
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1996 Volume 48 Issue 2 Pages 333-350
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- Published: 1996 Received: November 11, 1993 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Correction information
Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) S. K. Donaldson, The orientation of Yang-Mills moduli spaces and 4-manifold topology, J. Differential Geom., 24 (1987), 397-428.
2) S. K. Donaldson and P. B. Kronheimer, The Geometry of Four Manifolds, Oxford Math. Monographs, 1990.
3) M. Freedman, The topology of four-dimensional manifolds, J. Differential Geom., 17 (1982), 357-453.
4) R. Friedman and J. Morgan, Smooth four-manifolds and complex surfaces, Ergeb. Math. Grenzgeb., Band 27, Springer, 1994.
5) R. Fintushel and R. Stern, Instanton homology of Seifert fibered homology three spheres, Proc. London Math. Soc., 61 (1990), 109-137.
6) R. Fintushel and R. Stern, Surgery on cusp neighborhoods and the geography of irreducible 4-manifolds, Invent. Math., 117 (1994), 455-523.
7) R. Gompf, Nuclei of Elliptic Surfaces, Topology, 30 (1991), 479-512.
8) R. Gompf, Sums of Elliptic Surfaces, J. Differential Geom., 34 (1991), 93-114.
9) R. Gompf and T. Mrowka, Irreducible Four Manifolds need not be complex, Ann. of Math., 138 (1993), 61-111.
10) I. Hambleton and R. Lee, Perturbation of equivariant moduli spaces, Math. Ann., 293 (1992), 17-37.
11) Y. Kametani and Y. Sato, 0-dimensional moduli spaces of stable rank 2 bundles and differentiable structures on regular elliptic surfaces, Tokyo J. Math., 17 (1994), 253-267.
12) Y. Kametani, Torus sum formula of simple invariants for 4-manifolds, Kodai Math. J., 16 (1993), 138-170.
13) Y. Kametani, The simple invariant and differentiable structures on the Horikawa surface, Tohoku Math. J., 47 (1995), 541-553.
14) Y. Kametani, A vanishing theorem of Donaldson invariants for torus sum, in preparation.
15) D. Kotschick, On connected sum decompositions of algebraic surfaces and their fundamental groups, Internat. Math. Res. Notices, 6 (1993), 179-182.
16) P. Lisca, On simply connected noncomplex 4-manifolds, J. Differential Geom., 38 (1993), 217-224.
17) R. Mandelbaum, Decomposing analytic surfaces, Proc. Georgia Topology Conference 1979, In Geometric Topology, pp. 147-218.
18) T. Matsumoto, Extension problem of diffeomorphisms of a 3-torus over some 4-manifolds, Hiroshima Math. J., 14 (1984), 189-201.
19) B. Moishezon, Complex surfaces and connected sums of complex projective planes, Lecture Notes in Math., 603, Springer, 1977.
20) J. M. Morgan and T. S. Mrowka, On the diffeomorphism classification of regular elliptic surfaces, Internat. Math. Res. Notices, 6 (1993), 183-184.
21) J. Morgan and K. O'Grady, Elliptic surfaces with Pg=1: Smooth Classification, Lecture Notes in Math., 1545, Springer, 1993.
22) P. Orlik, Seifert manifolds, Lecture Notes in Math., 291, Springer, 1972.
23) P. S. Pao, The topological structure of 4-manifolds with effective torus actions I, Trans. Amer. Math. Soc., (1977), 279-317.
24) S. P. Plotnick, Equivariant intersection forms, knots in S4, and rotations in 2-spheres, Trans. Amer. Math. Soc., 296 (1986), 543-574.
25) F. Quinn, Ends of maps III: dimensions 4 and 5, J. Differential Geom., 17 (1982), 353-424.
26) M. Ue, A remark on the simple invariants for elliptic surfaces and their exotic structures not coming from complex surfaces, preprint (1991).
Right : [1] S. K. Donaldson, The orientation of Yang-Mills moduli spaces and 4-manifold topology, J. Differential Geom., 24 (1987), 397-428.
[2] S. K. Donaldson and P. B. Kronheimer, The Geometry of Four Manifolds, Oxford Math. Monographs, 1990.
[3] M. Freedman, The topology of four-dimensional manifolds, J. Differential Geom., 17 (1982), 357-453.
[4] R. Friedman and J. Morgan, Smooth four-manifolds and complex surfaces, Ergeb. Math. Grenzgeb., Band 27, Springer, 1994.
[5] R. Fintushel and R. Stern, Instanton homology of Seifert fibered homology three spheres, Proc. London Math. Soc., 61 (1990), 109-137.
[6] R. Fintushel and R. Stern, Surgery on cusp neighborhoods and the geography of irreducible 4-manifolds, Invent. Math., 117 (1994), 455-523.
[7] R. Gompf, Nuclei of Elliptic Surfaces, Topology, 30 (1991), 479-512.
[8] R. Gompf, Sums of Elliptic Surfaces, J. Differential Geom., 34 (1991), 93-114.
[9] R. Gompf and T. Mrowka, Irreducible Four Manifolds need not be complex, Ann. of Math., 138 (1993), 61-111.
[10] I. Hambleton and R. Lee, Perturbation of equivariant moduli spaces, Math. Ann., 293 (1992), 17-37.
[11] Y. Kametani and Y. Sato, 0-dimensional moduli spaces of stable rank 2 bundles and differentiable structures on regular elliptic surfaces, Tokyo J. Math., 17 (1994), 253-267.
[12] Y. Kametani, Torus sum formula of simple invariants for 4-manifolds, Kodai Math. J., 16 (1993), 138-170.
[13] Y. Kametani, The simple invariant and differentiable structures on the Horikawa surface, Tôhoku Math. J., 47 (1995), 541-553.
[14] Y. Kametani, A vanishing theorem of Donaldson invariants for torus sum, in preparation.
[15] D. Kotschick, On connected sum decompositions of algebraic surfaces and their fundamental groups, Internat. Math. Res. Notices, 6 (1993), 179-182.
[16] P. Lisca, On simply connected noncomplex 4-manifolds, J. Differential Geom., 38 (1993), 217-224.
[17] R. Mandelbaum, Decomposing analytic surfaces, Proc. Georgia Topology Conference 1979, In Geometric Topology, pp. 147-218.
[18] T. Matsumoto, Extension problem of diffeomorphisms of a 3-torus over some 4-manifolds, Hiroshima Math. J., 14 (1984), 189-201.
[19] B. Moishezon, Complex surfaces and connected sums of complex projective planes, Lecture Notes in Math., 603, Springer, 1977.
[20] J. M. Morgan and T. S. Mrowka, On the diffeomorphism classification of regular elliptic surfaces, Internat. Math. Res. Notices, 6 (1993), 183-184.
[21] J. Morgan and K. O'Grady, Elliptic surfaces with pg=1: Smooth Classification, Lecture Notes in Math., 1545, Springer, 1993.
[22] P. Orlik, Seifert manifolds, Lecture Notes in Math., 291, Springer, 1972.
[23] P. S. Pao, The topological structure of 4-manifolds with effective torus actions I, Trans. Amer. Math. Soc., (1977), 279-317.
[24] S. P. Plotnick, Equivariant intersection forms, knots in S4, and rotations in 2-spheres, Trans. Amer. Math. Soc., 296 (1986), 543-574.
[25] F. Quinn, Ends of maps III: dimensions 4 and 5, J. Differential Geom., 17 (1982), 353-424.
[26] M. Ue, A remark on the simple invariants for elliptic surfaces and their exotic structures not coming from complex surfaces, preprint (1991).
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