Geometric construction of classes in van Daele's K-theory
Abstract
We describe explicit generators for the "real" K-theory of "real" spheres in van Daele's picture. Pulling these generators back along suitable maps from tori to spheres produces a family of Hamiltonians used in the physics literature on topological insulators. We compute their K-theory classes geometrically, based on wrong-way functoriality of K-theory and the geometric version of bivariant K-theory, which we extend to the "real" case.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.