The Homotopy Type of Seiberg-Witten Configuration Space
Let X be a closed smooth 4-manifold. In the Theory of the Seiberg-Witten Equations, the configuration space is A_{alpha} imes 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 pos...
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| Format: | Article |
| Language: | English |
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Sociedade Brasileira de Matemática
2004-11-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
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| Online Access: | http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/7482/4303 |
| Summary: | Let X be a closed smooth 4-manifold. In the Theory of the Seiberg-Witten Equations, the configuration space is A_{alpha} imes 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} imes G_{alpha} Gamma(S_{alpha}^+) has the same homotopic type of the Jacobian TorusT^{b_1}(X)=frac{H^1(X;R)}{H^1(X;Z)};where b_1(X) = dim_R H_1(X;R). |
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| ISSN: | 0037-8712 2175-1188 |