Here’s a flowchart I made while preparing for an upcoming talk. I fear that it may be hard to follow without being already familiar with the story, but there’s little harm in posting it. Maybe it’ll help someone navigate the literature.
Image may be NSFW.
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Some context: Image may be NSFW.
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Note that $MU^*(-)$ is the universal complex-orientable cohomology theory.
Summary of the relationship of $MU^*$ and $L$:
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