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Homotopy theory is an important sub-field of algebraic topology. It is mainly concerned with the properties and structures of spaces which are invariant under homotopy. Chief among these are the homotopy groups of spaces, specifically those of spheres. Homotopy theory includes a broad set of ideas and techniques, such as cohomology theories, spectra and stable homotopy theory, model categories, spectral sequences, and classifying spaces.
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An open ended question: The dual of a covering map? Is this a real thing?
Reposted from this Reddit post as I didn't get good answers there:
So I've been reading about the Galois theory of covering maps and been staring at this equation for way too long:
$$\left| \pi_1(X,x_ …