27. The Eilenberg-Zilber Theorem
In this lecture we took advantage of the heavy machinery from the end of last semester (The Acyclic Models Theorem from Lecture 23) to prove the Eilenberg-Zilber Theorem. Along the way we needed a discussion about when chain maps between free chain complexes induce chain equivalences.
We will use the Acyclic Models Theorem several times this semester. For those of you who are already looking ahead to the Algebraic Topology II exam, fear not: the proof of the Acyclic Models Theorem will not be examinable—you need only know how to apply it. 🤓
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