We construct a stable homotopy refinement of quantum annular homology, a link homology theory introduced by Beliakova, Putyra and Wehrli. For each $r\geq ~2$ we associate to an annular link $L$ a naive $\mathbb {Z}/r\mathbb {Z}$-equivariant spectrum whose cohomology is isomorphic to the quantum annular homology of $L$ as modules over $\mathbb {Z}[\mathbb {Z}/r\mathbb {Z}]$. The construction relies on an equivariant version of the Burnside category approach of Lawson, Lipshitz and Sarkar. The quotient under the cyclic group action is shown to recover the stable homotopy refinement of annular Khovanov homology. We study spectrum level lifts of structural properties of quantum annular homology.

我们构建了量子环同源性的稳定同伦细化，这是由Beliakova，Putyra和Wehrli引入的链接同源性理论。对于每个$ r \ geq〜2 $，我们将其关联到一个环形链接$ L $一个幼稚的$ \ mathbb {Z} / r \ mathbb {Z} $-等变谱，其同调性与$ L $的量子环形同构同构作为$ \ mathbb {Z} [\ mathbb {Z} / r \ mathbb {Z}] $之上的模块。构造依赖于Lawson，Lipshitz和Sarkar的Burnside类方法的等变版本。显示在环状基团作用下的商可恢复环形科沃诺夫同源性的稳定的同伦精细化。我们研究了量子环同源性的结构性质的谱级提升。