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Title:
Higher degree of the covering monopole map in non commutative geometry
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Abstract:
I will introduce a monopole map over the universal covering space of a compact four manifold. In particular we formulate higher degree of the covering monopole map when the linearized map is isomorphic, which induces a homomorphism between K theory of group C^* algebras. As an application we propose an aspherical inequality on compact aspherical four manifolds. This presents a stronger version to 10/8 inequality by Furuta, in the aspherical class of four manifolds. This holds for many cases which include aspherical spin with residually finite fundamental groups. Technically the construction of the covering monopole map requires non linear estimates in Sobolev spaces and will motivate L^p analysis on non compact manifolds.
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