Abstract
AssumeF is the curvature (field) of a connection (potential) onR 4 with finiteL 2 norm\(\left( {\int\limits_{R^4 } {\left| F \right|^2 dx< \infty } } \right)\). We show the chern number\(c_2= {1 \mathord{\left/ {\vphantom {1 8}} \right. \kern-\nulldelimiterspace} 8}\pi ^2 \int\limits_{R^4 } {F \wedge} F\) (topological quantum number) is an integer. This generalizes previous results which showed that the integrality holds forF satisfying the Yang-Mills equations. We actually prove the natural general result in all even dimensions larger than 2.
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Communicated by S.-T. Yau
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Uhlenbeck, K.K. The Chern classes of Sobolev connections. Commun.Math. Phys. 101, 449–457 (1985). https://doi.org/10.1007/BF01210739
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DOI: https://doi.org/10.1007/BF01210739