Abstract
Let M 2n be a compact, oriented, differentiable manifold and U ⊂ M an oriented, differentiable submanifold of codimension two. Let u ∈ H 2(M; ℤ) be the Poincarédual cohomology class of the fundamental cycle of U. Further, let TU and TM be the tangent bundles of U, resp. M,and let NU be the normal bundle of U in M. By choosing a Riemannian metric we get an isomorphism TU ⊕ NU ≉ TM| U and NU gets the structure of an O(2)-bundle. Since M and U are oriented, the structure group of NU can be further reduced to SO(2) ≅ U(1).
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© 1994 Springer Fachmedien Wiesbaden
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Hirzebruch, F., Berger, T., Jung, R. (1994). A universal addition theorem for genera. In: Manifolds and Modular Forms. Aspects of Mathematics, vol 20. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-10726-2_3
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DOI: https://doi.org/10.1007/978-3-663-10726-2_3
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-528-16414-0
Online ISBN: 978-3-663-10726-2
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