HKR characters and higher twisted sectors

An introduction to HKR character theory

The generalized character theory of Hopkins, Kuhn, and Ravenel is an important tool in the study of Morava E-theory and higher height phenomena in chromatic homotopy theory. In this paper, we provide an introduction to HKR character theory with many examples, applications, and alternative points of view.

（扭曲微分）非阿贝尔上同调中的特征映射

The character map in (twisted differential) non-abelian cohomology

本文将K理论上的Chern特征推广至（扭曲、微分）非阿贝尔上同调，利用有理同伦论构建特征映射，统一并推广了Chern-Weil等同态，并在twistorial Cohomotopy理论中揭示了与M理论通量电荷量子化相关的拓扑关系。

Transchromatic twisted character maps

Refinements of the transchromatic generalized character maps are constructed by taking into account the torus action on the inertia groupoid (also known as the Fix functor). The relationship between this construction and the geometry of p-divisible groups is made precise.

Twisted differential K-characters and D-branes

We analyse in detail the language of partially non-abelian Deligne cohomology and of twisted differential K-theory, in order to describe the geometry of type II superstring backgrounds with D-branes. This description will also provide the opportunity to show some mathematical results of independent interest. In particular, we begin classifying the possible gauge theories on a D-brane or on a stack of D-branes using the intrinsic tool of long exact sequences. Afterwards, we recall how to construct two relevant models of differential twisted K-theory, paying particular attention to the dependenc…

Supersymmetric field theories from twisted vector bundles

We give a description of the delocalized twisted cohomology of an orbifold and the Chern character of a twisted vector bundle in terms of supersymmetric Euclidean field theories. This includes the construction of a twist functor for $1|1$-dimensional EFTs from the data of a gerbe with connection.

Families index theorem in supersymmetric WZW model and twisted K-theory: The SU(2) case

The construction of twisted K-theory classes on a compact Lie group is reviewed using the supersymmetric Wess-Zumino-Witten model on a cylinder. The Quillen superconnection is introduced for a family of supercharges parametrized by a compact Lie group and the Chern character is explicitly computed in the case of SU(2). For large euclidean time, the character form is localized on a D-brane.