论文标题
量子环同源性的稳定同型精致
Stable homotopy refinement of quantum annular homology
论文作者
论文摘要
我们构建了量子环同源性的稳定同型精炼，这是Beliakova，Putyra和Wehrli引入的链接同源理论。对于每个$ r \ geq 2 $，我们将与环链$ l $ a naive $ \ mathbb {z}/r \ mathbb {z} $ - equivariant spectrum spectrum同构成$ l $的量子同型，作为$ l $的量子，是$ l $ $ \ mathbb {z} [\ mathbb {z}/r \ mathbb {z}] $。该构建依赖于劳森，Lipshitz和Sarkar的Burnside类别方法的模棱两可的版本。循环群体作用下的商显示恢复了环形霍瓦诺夫同源性的稳定同质性细化。我们研究量子环同源性结构特性的光谱水平升力。
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.
