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Covering monopole map and higher degree ...
Kato, Tsuyoshi...

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Covering monopole map and higher degree in non commutative geometry by Kato, Tsuyoshi ( Author )
Lemonjar Open Access
Australian National University
08-08-2023
In this paper we develop analysis of the monopole maps over the universal covering space of a compact four manifold. We induce a property on local properness of the covering monopole map under the condition of closeness of the AHS complex. In particular we construct a higher degree of the covering monopole map when the linearized equation is isomorphic, which induces a homomorphism between K group of the group C^* algebras. It involves non linear analysis on the covering space, which is related to L^p cohomology. We also obtain various Sobolev estimates on the covering spaces. As a possible application, we propose an aspherical version of 10/8 inequality, combining with Singer conjecture on L^2 cohomology. It is satisfied for a large class of four manifolds which includes some complex surfaces of general type.
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Article
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29.34 KB
English
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MYR 0.01
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http://arxiv.org/abs/1606.02402
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