Gluing formulae for Donaldson invariants for connected sums along surfaces

Details Gluing formulae for Donaldson invariants for connected sums along surfaces Gluing formulae for Donaldson invariants for connected sums along surfaces

1997-02-06

arxiv.org/abs/dg-ga/9702002v1

Mathematics

Differential Geometry

18 pages, Latex (Latex2e)

Scientific paper

We solve a conjecture of Morgan and Szabo (Embedded genus 2 surfaces in four-manifolds, Preprint) about the relationship of the basic classes of two four-manifolds $X_i$ of simple type with $b_1=0$, $b^+>1$, such that there are embedded Riemann surfaces of genus $g \geq 2$ and self-intersection zero (and representing odd homology classes) with the basic classes of the manifold X which appears as a connected sum along the surfaces (supposing this latter one is of simple type). This is also expressed as constraints in the basic classes of X. The result is in accordance with the results on Seiberg-Witten invariants (Morgan, Szabo and Taubes, A product formula for the Seiberg-Witten invariants and the generalized Thom conjecture).

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