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Scalar curvature and connected sums of self-dual 4-manifolds

Mustafa Kalafat (2011)

Journal of the European Mathematical Society

Under a reasonable vanishing hypothesis, Donaldson and Friedman proved that the connected sum of two self-dual Riemannian 4-manifolds is again self-dual. Here we prove that the same result can be extended to the positive scalar curvature case. This is an analogue of the classical theorem of Gromov–Lawson and Schoen–Yau in the self-dual category. The proof is based on twistor theory.

Schur and Schubert polynomials as Thom polynomials-cohomology of moduli spaces

László Fehér, Richárd Rimányi (2003)

Open Mathematics

The theory of Schur and Schubert polynomials is revisited in this paper from the point of view of generalized Thom polynomials. When we apply a general method to compute Thom polynomials for this case we obtain a new definition for (double versions of) Schur and Schubert polynomials: they will be solutions of interpolation problems.

Seiberg-Witten invariants, the topological degree and wall crossing formula

Maciej Starostka (2012)

Open Mathematics

Following S. Bauer and M. Furuta we investigate finite dimensional approximations of a monopole map in the case b 1 = 0. We define a certain topological degree which is exactly equal to the Seiberg-Witten invariant. Using homotopy invariance of the topological degree a simple proof of the wall crossing formula is derived.

Seiberg-Witten Theory

Jürgen Eichhorn, Thomas Friedrich (1997)

Banach Center Publications

We give an introduction into and exposition of Seiberg-Witten theory.

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