Jacob Lurie : Higher Topos Theory

Higher Topos Theory

On the Classification of Topological Field Theories (Draft)

1 Topological Field Theories and Higher Categories 2 1.1 Classical Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Extending Down: Lower Dimensional Manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 Higher Category Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.4 Extending Up: Diffeo...

On the Classification of Topological Field Theories

1 Topological Field Theories and Higher Categories 2 1.1 Classical Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Extending Down: Lower Dimensional Manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 Higher Category Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.4 Extending Up: Diffeo...

Characters in Global Equivariant Homotopy Theory

Realizing Families of Landweber Exact Homology Theories

I discuss the problem of realizing families of complex orientable homology theories as families of E ∞-ring spectra, including a recent result of Jacob Lurie emphasizing the role of p-divisible groups. A few years ago, I wrote a paper [10] discussing a realization problem for families of Landweber exact spectra. Since Jacob Lurie [27] now has a major positive result in this direction, it seems ...