Abstract
The Chern classes appearing in Serre’s letter to Borel of Chap. 44 are particular characteristic classes, that is, certain cohomology classes measuring the way in which the fibres of a fibre bundle “fit together over the whole manifold”, as written by Whitney at the end of the next excerpt from the introduction to his 1937 paper [193]
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Notes
- 1.
The modern definition, through atlases, of an abstract smooth manifold of arbitrary dimension, seems to have been published for the first time in Veblen and Whitehead’s 1931 paper [176]. It was slightly modified and further explored in Whitney’s 1936 paper [192]. One may find details about those papers in Chorlay’s commented selection [44] of foundational articles on differential geometry and topology.
References
R. Chorlay, Géométrie et topologie différentielles (1918–1932) (Hermann, Paris, 2015). A commented selection of articles
O. Veblen, J.H.C. Whitehead, A set of axioms for differential geometry. Proc. Natl. Acad. Sci. 17 (10), 551–561 (1931). With an Erratum on page 660
H. Whitney, Differentiable manifolds. Ann. Math. 37 (3), 645–680 (1936)
H. Whitney, Topological properties of differentiable manifolds. Bull. Am. Math. Soc. 43, 785–805 (1937)
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Popescu-Pampu, P. (2016). Whitney and the Cohomology of Fibre Bundles. In: What is the Genus?. Lecture Notes in Mathematics(), vol 2162. Springer, Cham. https://doi.org/10.1007/978-3-319-42312-8_46
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DOI: https://doi.org/10.1007/978-3-319-42312-8_46
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