Khovanov homology is an unknot-detector
Khovanov homology is an unknot-detector
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霍瓦诺夫同源性是一个未知检测器
DOI：
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发表时间：
2010
期刊：
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通讯作者：
T. Mrowka
中科院分区：
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作者：
P. Kronheimer;T. Mrowka
我们证明一个结是解结当且仅当它的约化Khovanov上同调为秩1。证明有两个步骤。我们首先证明了谱序列从约化Khovanov上同调开始，并与用奇异实例定义的结同调邻接。然后我们证明后者同构于缝合结补的瞬时花同构：一个已知用于检测解结的不变量。
We prove that a knot is the unknot if and only if its reduced Khovanov cohomology has rank 1. The proof has two steps. We show first that there is a spectral sequence beginning with the reduced Khovanov cohomology and abutting to a knot homology defined using singular instantons. We then show that the latter homology is isomorphic to the instanton Floer homology of the sutured knot complement: an invariant that is already known to detect the unknot.