Twists of K-theory and TMF

Understand

We explore an approach to twisted generalized cohomology from the point of view of stable homotopy theory and quasicategory theory provided by arXiv:0810.4535.

• We explain the relationship to the twisted K-theory provided by Fredholm bundles.
• We show how our approach allows us to twist elliptic cohomology by degree four classes, and more generally by maps to the four-stage Postnikov system BO<0...4>.
• We also discuss Poincare duality and umkehr maps in this setting.