Covering monopole map and higher degree in non commutative geometry

2016/06/08 by Tsuyoshi Kato, Kato, Tsuyoshi · 2 citations
Mathematics · #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1606.02402

openalex publication_date 2016/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 L² cohomology. It is satisfied for a large class of four manifolds which includes some complex surfaces of general type.

Citations

• On the signatures of even 4-manifolds

Cited by

• L² harmonic theory, Seiberg-Witten theory and asymptotics of differential forms
• Higher Nahm transform in non commutative geometry

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