<b>The Homotopy Type of Seiberg-Witten Configuration Space</b> - doi: 10.5269/bspm.v22i2.7482

Abstract

Let X be a closed smooth 4-manifold. In the Theory of the Seiberg-Witten Equations, the configuration space is A{\alpha}\times g_{\alpha} \Gamma(S_{\alpha}^+ ), where A_{\alpha} is defined
as the space of u_1-connections on a complex line bundle over X, \Gamma(S_{\alpha}^+) is the space of sections of the positive complex spinor bundle over X and G_{\alpha} is the gauge group.
It is shown that A_{\alpha} \times g_{\alpha}\Gamma(S_{\alpha}^+) has the same homotopic type of the Jacobian Torus T^{b1(X)} = \frac{H1(X;R)}{H1(X; Z)} ;where b_1(X) = dim_{R}H^1(X;R).