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Curvature forms with singularities and non-integral characteristic classes
| Content Provider | Semantic Scholar |
|---|---|
| Author | Asada, Akira |
| Copyright Year | 1985 |
| Abstract | Xntrodllction This is the detailed exposition of [7]. The outline of the paper is as follows: In gl, we define the 2rtlimensional non-abelian de Rham set Hi (M, "'). Here M is a smooth manifold and fi is the sheaf of germs of smooth matrix valued 1forms e such that dO+eAO==O. A bijection between H' (ML a') and a set of special classes of matrix valued 2-forms on M are also defined. In a sense, these, 2-forms can be regarded as curvature forms with singularities (singular gauge fields) (cf. [11], [17], [23], [24], [25]). Since we have obtained 2-dimensional non-abelian Poincar6 lemma (local integration theorem of the eguation de + 0A e = e, [10]), the results of this section will be improved in future. In ss2, we define the cohomology sets H2 (Ml Gt) and H2 (M; Gd), G==GL (n, C). Here Gt and Gd are sheaves of germs of constant and smmooth G-valued functions on M; respectively. Then we show the exactness of the following sequence |
| Starting Page | 145 |
| Ending Page | 169 |
| Page Count | 25 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/BFb0074582 |
| Volume Number | 20 |
| Alternate Webpage(s) | https://soar-ir.repo.nii.ac.jp/index.php?action=pages_view_main&active_action=repository_action_common_download&attribute_id=65&block_id=45&file_no=1&item_id=12130&item_no=1&page_id=13 |
| Alternate Webpage(s) | https://doi.org/10.1007/BFb0074582 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
