Algebraic $K$-theory, cohomotopy $K$-groups, and Koszul duality

Xiaojun Chen, Farkhod Eshmatov, Maozhou Huang

Let $A$ be an augmented differential graded algebra over a field $k$ of characteristic zero, and let $A^{!}=\mathbf{R}{\mathrm{Hom}}_A(k,k)$ be its Koszul dual algebra. Blumberg and Ma…