Abstract
The moduli spaces of instantons over a compact 4-manifold X carry a great deal of differential-topological information leading to many invariants of X. In some simple cases these invariants are just numbers, obtained by counting points in O-dimensional spaces moduli spaces, but more generally one gets polynomial functions on the homology, particularly the 2-dimensional homology, of X. To any homology class ∑ ∈ H 2(X) one associates a cohomology class μ(∑) over the moduli space and, assuming that this is even dimensional, one can then evaluate the top-dimensional power of μ(∑) on the moduli space.
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References
M.F. Atiyah, New Invariants for 3 and 4-dimensional manifolds, Proc. Sympos. Pure Math. 48 (1988).
M.F. Atiyah, Topological Quantum Field Theories, Publ. Math. IHES, 68 (1988).
M. F. Atiyah, V. Patodi & I. M. Singer, Spectral asymetry and Riemannian geometry II & III, Math. Proc. Camb. Phil. Soc, 78 & 79 (1975), pp. 71–99, 405–32.
D. Austin & P. Braam, Equivariant Floer thoery and Donaldson Polynomials, in preparation.
D. Austin & P. Braam, Morse-Bott theory and equivariant cohomology, in this volume.
P. Deligne, P. Griffiths, J. Morgan & D. Sullivan, Homotopy Theory of Compact Kähler Manifolds, Inv. Math. 29 (1973), pp. 245–274.
S.K. Donaldson, Polynomial Invariants for smooth four-manifolds, Topology 29 (1990), pp. 257–315.
S.K. Donaldson, Gluing techniques in the cohomology of moduli spaces, to appear in the volume in honour of Milnor’s sixtieth birthday, Publish and Perish.
S.K. Donaldson, The orientation of Yang-Mills moduli spaces and four-manifold topology, J. Diff. Geom., 24 (1987), pp. 397–428.
S.K. Donaldson, Irrationality and the h-cobordism conjecture, J. Diff. Geom. 26 (1987), pp. 141–168.
S.K. Donaldson, M. Furuta & D. Kotschick, Floer Homology Groups in Yang-Mills Theory, in preparation.
S.K. Donaldson & P.B.K. Kronheimer, The Geometry of 4-Manifolds, Oxford University Press, Oxford, 1990.
S. Dostoglou & D. Salamon, Instanton Homology and Symplectic Fixed Points, preprint.
A. Floer, An instanton invariant for 3-manifolds, Comm. Math. Phys. 118 (1988), 215–240.
M. Furuta, unpublished manuscript.
M. Furuta, Morse theory and Thom-Gysin exact sequence, preprint.
K. Fukaya, Instanton Homology for Oriented 3-Manifolds, to appear in Adv. Studies in Pure Mathematics, ed Y. Matsumoto & S. Morita.
D. Salamon, Morse theory, the Conley index and Floer homology, Bull. London Math. Soc. 22 (1990), pp. 113–140.
D. Sullivan, Infinitesimal computations in Topology, Publ. IHES Vol 47 (1978), pp. 261–331.
C.H. Taubes, Gauge Theory on Asymptotically Periodic 4-Manifolds, J. Diff. Geom. 25 (1987), pp. 363–430.
C.H. Taubes, A simplicial model for Donaldson-Floer theory, in this volume.
M. Thaddeus, Conformal Field Theory and the Cohomology of the Moduli Space of Stable Bundles, J. Diff. Geom. 35, 1 (1992), pp. 131–150.
E. Witten, Topological Quantum Field Theory, Comm. Math. Phys., 117 (1988), pp. 353–386.
E. Witten, Two dimensional gravity and intersection theory on moduli space, Surveys in Diff. Geom. 1 (1991), pp. 243 ff.
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© 1995 Birkhäuser Verlag
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Braam, P.J., Donaldson, S.K. (1995). Fukaya-Floer homology and gluing formulae for polynomial invariants. In: Hofer, H., Taubes, C.H., Weinstein, A., Zehnder, E. (eds) The Floer Memorial Volume. Progress in Mathematics, vol 133. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9217-9_11
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