Global homotopy theory / Lecture 14: Left and right induced global homotopy types

Lecture 14 of "Global homotopy theory": We study the embeddings of the non-equivariant stable homotopy category into the global stable homotopy category via the left and right adjoints to the forgetful functor. The 'left induced' global homotopy types are characterized by constant geometric fixed points; the 'right induced' global homotopy types represent global Borel cohomology theories.

Contents:
00:13 Review of lecture 13
02:50 The left adjoint as the action on the global sphere spectrum: model category version
06:55 The left adjoint as the action on the global sphere spectrum: ∞-category version
08:31 Left and right induced orthogonal spectra
10:53 Characterization of left induced spectra by constant geometric fixed points
13:41 Proof of the left characterization
21:43 Equivariant cohomology theories
24:32 Characterization of right induced spectra by cofreeness property
26:37 Right induced spectra represent Borel cohomology theories
29:14 Right induced spectra are cofree
32:03 Cofree spectra are right induced
41:46 Homotopy global functors of right induced spectra
48:29 Review of global K-theory
57:15 Global K-theory is right induced from finite cyclic groups
59:21 The Atiyah-Segal completion theorem
1:03:18 Carlsson's theorem (aka the Segal conjecture)

For more information about the class, such as the topics, prerequisites, or references, visit the webpage: