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1 Algebraic Topology Part III, 2015-16: Sheet 4 1. ...
https://www.dpmms.cam.ac.uk/study/III/Algebraic%20Topology/2018-2019/AT(III)2018-sheet4.pdf21 Nov 2018: form over R is equivalent to a direct sum of copies of the form(. ... b) Prove that if E and F are oriented vector bundles over a space X, their Euler classessatisfy eEF = eE eF. -
1 Algebraic Topology Part III, 2018-19: Sheet 3 1. ...
https://www.dpmms.cam.ac.uk/study/III/Algebraic%20Topology/2018-2019/AT(III)2018-sheet3.pdf11 Nov 2018: bundle of realrank one) over the circle, and prove that bundle is non-trivial. ... 7. Let p : E B be a fibre bundle over a path-connected space B with fibre F = p1(b).Suppose that H(F) is finitely generated and free, and that
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