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Here are some links to proofs about homotopy theory, formalized in homotopy type theory. Please add!
Maybe we could figure out a way not to duplicate stuff between this page and homotopy groups of spheres?
Ali: Results about homotopy groups of spheres should go there, everything else here.
Cast of characters so far: Jeremy Avigad, Guillaume Brunerie, Favonia, Eric Finster, Chris Kapulkin, Dan Licata, Peter Lumsdaine, Mike Shulman, Evan Cavallo
cohomology * To do cohomology with finite coefficients, all we need is the boring work of defining as an explicit group. * Calculate some more cohomology groups. * Compute the loop space of this construction and use it to define spectra.
Eilenberg-MacLane space * Dan’s construction. * is a spectrum, formalized
cohomology * Deriving cohomology theories from spectra * Mayer-Vietoris sequence, with exposition * Cohomology of the n-torus, which could be easily extended to any finite product of spheres.
Implies Freudenthal suspension theorem? Implies whenever whenever
van Kampen theorem * Mike’s proofs are in the book and Favonia formalized it. {{deadlink}}
Covering space? * Favonia’s proofs (link in flux due to library rewrite).
Blakers-Massey theorem?
Revision on January 19, 2019 at 19:06:38 by Ali Caglayan. See the history of this page for a list of all contributions to it.