The Global Orbit Category and Assembly Maps
Date:
I gave this talk at the Binghamton University Graduate Combinatorics, Algebra, and Topology (BUGCAT) Conference in 2025.
We explored the global orbit ∞-category \(Orb\) of arbitrary discrete groups. We began by showing the orbit (1-)category \(\mathcal{O}(G)\) for a fixed \(G\) can be identified with the slice ∞-category \(Orb_{/G}\). We then used this equivalence to give purely categorical proofs for known results about assembly maps, like the transitivity principle.