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Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras

5 votes
2 answers
430 views

K-theory of a coconnective dga

I have seen somewhere that if a differential graded algebra $A$ is connective (homologically graded), then the Grothendieck group $K_{0}(A)=K_{0}(H_{0}(A))$. Suppose that $A$ is a differential graded …
4 votes
1 answer
193 views

Split cofibrations up to quasi-isomorphism

$R$ a ring $(1\neq 0)$, $\mathbf{Perf}(R)$ is the category of perfect complexes (of right $R$-modules). Suppose that $A_{\bullet}\rightarrow B_{\bullet}\rightarrow B_{\bullet}/A_{\bullet}$ a short e …