论文标题
（扭曲的差异）非阿布尔共同体中的角色图
The character map in (twisted differential) non-abelian cohomology
论文作者
论文摘要
我们将Chern特征扩展到K-Theory上的概括，以概括为Chern-dold特征在广义的共同体学理论上，进一步延伸到（扭曲的，差异）非阿布莱恩的共同体学理论，其中其目标是非亚洲DE RHAM共同的共同体，是扭曲的L------------- l-infinity l-Infinity Algebra估算差异差异的形式。该构建相当于利用DG代数有理同义理论的基本定理，以扭曲的DE RHAM定理的非 - 亚伯利亚概括。我们表明，非亚伯语角色除了Chern-dold角色外，还复制了Chern-Weil同质性以及其次要的Cheeger-Simons对（差异）非亚伯利亚共同学的同态同构，在1级中，以原理套件（与连接）表示。因此，将所有这些都推广到更高（扭曲的，差异）的非亚伯式同胞，以较高的束/更高的Gerbes表示（具有较高的连接）。作为一个基本示例，我们讨论了8个模型上的扭曲共同体理论的扭曲的非亚洲角色图，这可以看作是4级拓扑模块化形式（TMF）的扭曲的非亚伯利亚增强。事实证明，这证明了在高能量物理学中列出了高级拓扑的列表，这些拓扑是在高度的拓扑范围内被认为是柔和的量化量量量的，并且是柔和的量化。
We extend the Chern character on K-theory, in its generalization to the Chern-Dold character on generalized cohomology theories, further to (twisted, differential) non-abelian cohomology theories, where its target is a non-abelian de Rham cohomology of twisted L-infinity algebra valued differential forms. The construction amounts to leveraging the fundamental theorem of dg-algebraic rational homotopy theory to a twisted non-abelian generalization of the de Rham theorem. We show that the non-abelian character reproduces, besides the Chern-Dold character, also the Chern-Weil homomorphism as well as its secondary Cheeger-Simons homomorphism on (differential) non-abelian cohomology in degree 1, represented by principal bundles (with connection); and thus generalizes all these to higher (twisted, differential) non-abelian cohomology, represented by higher bundles/higher gerbes (with higher connections). As a fundamental example, we discuss the twisted non-abelian character map on twistorial Cohomotopy theory over 8-manifolds, which can be viewed as a twisted non-abelian enhancement of topological modular forms (tmf) in degree 4. This turns out to exhibit a list of subtle topological relations that in high energy physics are thought to govern the charge quantization of fluxes in M-theory.
