COHOMOLOGY OF FLAT PRINCIPAL BUNDLES
- Authors
- Byun, Yanghyun; Kim, Joohee
- Issue Date
- Aug-2018
- Publisher
- CAMBRIDGE UNIV PRESS
- Keywords
- flat principal bundle; de Rham cohomology; adjoint bundle
- Citation
- PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, v.61, no.3, pp.869 - 877
- Indexed
- SCIE
SCOPUS
- Journal Title
- PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY
- Volume
- 61
- Number
- 3
- Start Page
- 869
- End Page
- 877
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/149553
- DOI
- 10.1017/S0013091517000475
- ISSN
- 0013-0915
- Abstract
- We invoke the classical fact that the algebra of bi-invariant forms on a compact connected Lie group G is naturally isomorphic to the de Rham cohomology H-dR(*)(G) itself. Then, we show that when a flat connection A exists on a principal G-bundle T, we may construct a homomorphism E-A : H-dR*(G) -> H-dR(*)(P), which eventually shows that the bundle satisfies a condition for the Leray-Ilirsch theorem. A similar argument is shown to apply to its adjoint bundle. As a corollary, we show that that both the flat principal bundle and its adjoint bundle have the real coefficient cohomology isomorphic to that of the trivial bundle.
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