Publication: Gluing formulae for Donaldson invariants for connected sums along surfaces.
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1997
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International Press
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Abstract
Following our work in [18], we prove a gluing formula for the Donaldson nvariants of the connected sum of two four-manifolds along surfaces of the same genus g, self-intersection zero and representing odd homology classes,solving a conjecture of Morgan and Szab´o [14].
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P. Braam and S. K. Donaldson, Fukaya-Floer homology and gluing formulae for polynomial invariants, The Floer memorial volume. Progress in mathematics, 133 1994, 257-281.
S. K. Donaldson, On the work of Andreas Floer, Jahresber. Deutsch. Math. Verein, 95 1993,103-120.
S. K. Donaldson, Floer homology and algebraic geometry, Vector bundles in algebraic geometry,London Math. Soc. Lecture Notes Series, 208 Cambridge University Press,Cambridge, 1995,119-138.
S. K. Donaldson and P. B. Kronheimer, The geometry of 4-manifolds, Oxford University Press,1990.
S. Dostoglou and D. Salamon, Self-dual instantons and holomorphic curves, Annals of Mathematics,139 1994, 581-640.
R. Fintushel and R. J. Stern, Donaldson invariants of 4-manifolds with simple type, Jour. Diff.Geometry, 42 1995,577-633.
A. Floer, Symplectic fixed points and holomorphic spheres, Comm. Math. Physics, 120 1989,575-611.
R. Friedman and J. W. Morgan, Smooth four-manifolds and complex surfaces, Springer-Verlag,1994.
A. D. King and P. E. Newstead, On the cohomology ring of the moduli space of rank 2 vector bundles on a curve,Liverpool Preprint, 1994.
D. Kotschick, SO(3) invariants for 4-manifolds with b+2 = 1, Proc. Lond. Math. Soc. 63 1991,426-448.
D. Kotschick and J. W. Morgan, SO(3) invariants for 4-manifolds with b+2 = 1 II, Jour. Differential Geometry, 39 1994, 433-456.
P. B. Kronheimer and T. S. Mrowka, Embedded surfaces and the structure of Donaldson’s polynomial invariants, Jour. Differential Geometry, 41 1995, 573-734.
J. W. Morgan and T. S. Mrowka, The smooth classification of elliptic surfaces, Conference Proceedings and Lecture Notes in Geometry and Topology, IV Geometry, Topology, and Physics
for Rauol Bott, International Press, 1995.
J. W. Morgan and Z. Szabo, Embedded genus 2 surfaces in four-manifolds, Preprint.
J. W. Morgan and Z. Szabo, Embedded tori in four-manifolds, Preprint.
J. W. Morgan, Z. Szabo and C. H. Taubes, A product formula for the Seiberg-Witten invariants and the generalized Thom conjecture, Preprint, 1995.
V. Muñoz, Oxford D. Phil. Thesis, Gauge Theory and Complex Manifolds, 1996.
V. Muñoz, Donaldson invariants for connected sums along Riemann surfaces of genus 2, Submitted to Topology.
A. Stipsicz, Donaldson series and (−1)-tori, Jour. Reine ange Math. 465 1995, 133-144.
Z. Szabo, Irreducible four-manifolds with small Euler characteristics, Topology. 35 1996, 411-426.
M. Thaddeus, Conformal field theory and the cohomology of the moduli space of stable bundles,Jour. Differential Geometry, 35 1992, 131-150.
E. Witten, Monopoles and four-manifolds, Mathematical Research Letters, 1 1994, 769-796.