# 33. Fibre bundles

In this lecture we introduce *fibre bundles*, and give some examples to show how ubiquitous they are. We then define *fibrations*, which are a homotopy-theoretic analogue of fibre bundles. We then state an important result that says fibre bundles are always (weak) fibrations. We will prove this in the last third of the course.

The second half of the lecture talks about modules and tensor products over a ring. We end up by proving that Corollary 32.9 from the last lecture continues to hold in this setting. This will be needed in the next lecture, when we state and prove the famous *Leray-Hirsch Theorem *which gives a method for computing the cohomology of fibre bundles.

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