Global homotopy theory / Lecture 4: The double coset formula

Lecture 4 of "Global homotopy theory": I illustrate the general double coset formula for the transfer followed by restriction to a closed subgroup by explaining several examples.

Contents:
00:10 Review of Lecture 3
04:33 Globally, the Weyl group action factors through outer automorphisms
11:03 The double coset formula for K=e
14:39 The double coset formula for H=e
16:16 The double coset formula for K=H normal in G
18:07 Example: G=Σ_3, H=A_3, K=(12)
19:52 Example: G=Σ_n, H=K=Σ_{n-1}
23:22 Case study: the example G=SO(3), H=SO(2), K=Σ_3
43:15 Exercise 3
44:56 A check sum formula
50:17 Summary: the natural structure on equivariant homotopy groups of orthogonal spectra
54:40 The global Burnside category

Blackboard typos:
- a misleading typo occurs beginning at 21:07 : of course, it is not correct that the conjugates of Σ_{n-1} by the transposition t=(n-1,n) are Σ_{n-2}; rather, the intersection of Σ_{n-1} and its t-conjugate is Σ_{n-2}
 - at 22:03, the restriction in the last term of the double coset formula should go down to Σ_{n-2}

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Special thanks to JDLP for the post production of this video