A topological manifold M of dimension n has a fundamental class denoted by w M or [M] ∈ H n (M,Z/2Z), and when it has an orientation, this class is defined in H n (M,Z) with the same notation. In each case, the cap product.
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Husemöller, D.: Fibre Bundles, 3rd ed. Springer-Verlag, New York (1994)
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© 2008 Springer-Verlag Berlin Heidelberg
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Husemöller, D., Joachim, M., Jurčo, B., Schottenloher, M. (2008). Characteristic Classes of Manifolds. In: Basic Bundle Theory and K-Cohomology Invariants. Lecture Notes in Physics, vol 726. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74956-1_12
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