2-torsion instanton invariants

Fintushel, Ronald; Stern, Ronald J.

doi:10.1090/S0894-0347-1993-1168958-8

$2$-torsion instanton invariants
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by Ronald Fintushel and Ronald J. Stern

J. Amer. Math. Soc. 6 (1993), 299-339

DOI: https://doi.org/10.1090/S0894-0347-1993-1168958-8

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References

Michael Atiyah, New invariants of $3$- and $4$-dimensional manifolds, The mathematical heritage of Hermann Weyl (Durham, NC, 1987) Proc. Sympos. Pure Math., vol. 48, Amer. Math. Soc., Providence, RI, 1988, pp. 285–299. MR 974342, DOI 10.1090/pspum/048/974342
M. F. Atiyah, V. K. Patodi, and I. M. Singer, Spectral asymmetry and Riemannian geometry. I, Math. Proc. Cambridge Philos. Soc. 77 (1975), 43–69. MR 397797, DOI 10.1017/S0305004100049410
M. F. Atiyah, V. K. Patodi, and I. M. Singer, Spectral asymmetry and Riemannian geometry. I, Math. Proc. Cambridge Philos. Soc. 77 (1975), 43–69. MR 397797, DOI 10.1017/S0305004100049410
S. K. Donaldson, Connections, cohomology and the intersection forms of $4$-manifolds, J. Differential Geom. 24 (1986), no. 3, 275–341. MR 868974
S. K. Donaldson, Polynomial invariants for smooth four-manifolds, Topology 29 (1990), no. 3, 257–315. MR 1066174, DOI 10.1016/0040-9383(90)90001-Z
S. K. Donaldson, Yang-Mills invariants of four-manifolds, Geometry of low-dimensional manifolds, 1 (Durham, 1989) London Math. Soc. Lecture Note Ser., vol. 150, Cambridge Univ. Press, Cambridge, 1990, pp. 5–40. MR 1171888
S. K. Donaldson and P. B. Kronheimer, The geometry of four-manifolds, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1990. Oxford Science Publications. MR 1079726
Ronald Fintushel and Ronald J. Stern, Instanton homology of Seifert fibred homology three spheres, Proc. London Math. Soc. (3) 61 (1990), no. 1, 109–137. MR 1051101, DOI 10.1112/plms/s3-61.1.109
Ronald Fintushel and Ronald J. Stern, Homotopy $K3$ surfaces containing $\Sigma (2,3,7)$, J. Differential Geom. 34 (1991), no. 1, 255–265. MR 1114462
Andreas Floer, An instanton-invariant for $3$-manifolds, Comm. Math. Phys. 118 (1988), no. 2, 215–240. MR 956166
Daniel S. Freed and Karen K. Uhlenbeck, Instantons and four-manifolds, Mathematical Sciences Research Institute Publications, vol. 1, Springer-Verlag, New York, 1984. MR 757358, DOI 10.1007/978-1-4684-0258-2
Robert Friedman and John W. Morgan, Complex versus differentiable classification of algebraic surfaces, Proceedings of the 1987 Georgia Topology Conference (Athens, GA, 1987), 1989, pp. 135–139. MR 1007985, DOI 10.1016/0166-8641(89)90050-3
Robert E. Gompf, Sums of elliptic surfaces, J. Differential Geom. 34 (1991), no. 1, 93–114. MR 1114454

Irreducible four manifolds need not be complex

Martin W. Liebeck, Cheryl E. Praeger, and Jan Saxl, The maximal factorizations of the finite simple groups and their automorphism groups, Mem. Amer. Math. Soc. 86 (1990), no. 432, iv+151. MR 1016353, DOI 10.1090/memo/0432
Richard Mandelbaum, Decomposing analytic surfaces, Geometric topology (Proc. Georgia Topology Conf., Athens, Ga., 1977) Academic Press, New York-London, 1979, pp. 147–217. MR 537731
Jack McLaughlin, Some subgroups of $\textrm {SL}_{n}\,(\textbf {F}_{2})$, Illinois J. Math. 13 (1969), 108–115. MR 237660

The

-moduli space on manifolds with cylindrical ends

A local Mayer-Vietoris principle for Yang-Mills moduli spaces

Yongbin Ruan, A universal constraint for Donaldson invariants, J. Differential Geom. 35 (1992), no. 3, 711–722. MR 1163456
Winfried Scharlau, Quadratic and Hermitian forms, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 270, Springer-Verlag, Berlin, 1985. MR 770063, DOI 10.1007/978-3-642-69971-9
Clifford Henry Taubes, Self-dual connections on $4$-manifolds with indefinite intersection matrix, J. Differential Geom. 19 (1984), no. 2, 517–560. MR 755237
Clifford Henry Taubes, Gauge theory on asymptotically periodic $4$-manifolds, J. Differential Geom. 25 (1987), no. 3, 363–430. MR 882829

-moduli spaces on

-manifolds with cylindrical ends

Karen K. Uhlenbeck, Connections with $L^{p}$ bounds on curvature, Comm. Math. Phys. 83 (1982), no. 1, 31–42. MR 648356
C. T. C. Wall, Diffeomorphisms of $4$-manifolds, J. London Math. Soc. 39 (1964), 131–140. MR 163323, DOI 10.1112/jlms/s1-39.1.131
C. T. C. Wall, On simply-connected $4$-manifolds, J. London Math. Soc. 39 (1964), 141–149. MR 163324, DOI 10.1112/jlms/s1-39.1.141
C. T. C. Wall, On the orthogonal groups of unimodular quadratic forms, Math. Ann. 147 (1962), 328–338. MR 138565, DOI 10.1007/BF01440955
C. T. C. Wall, On the orthogonal groups of unimodular quadratic forms. II, J. Reine Angew. Math. 213 (1963/64), 122–136. MR 155798, DOI 10.1515/crll.1964.213.122