论文标题
漂浮物同源性和非纤维结检测
Floer homology and non-fibered knot detection
论文作者
论文摘要
我们首次证明了Floer同源性和Khovanov同源性可以检测到无纤维结的结，而Homfly同源性检测到无限的许多这样的结。以前已知这些理论仅检测一个六节，全部均具有纤维。这些结果依赖于我们的主要技术定理，该定理在三个球体中对属1节进行了完整的分类，其结中的浮子同源性在Alexander顶部分级是二维。我们讨论了该分类在Dehn手术中的问题的应用，这些问题是在两个续集中进行的。其中包括一个证据，表明$ 0 $ - 手术的特征是无限的结，从1987年对财产的决议中概括了Gabai的结果。
We prove for the first time that knot Floer homology and Khovanov homology can detect non-fibered knots, and that HOMFLY homology detects infinitely many such knots; these theories were previously known to detect a mere six knots, all fibered. These results rely on our main technical theorem, which gives a complete classification of genus-1 knots in the 3-sphere whose knot Floer homology in the top Alexander grading is 2-dimensional. We discuss applications of this classification to problems in Dehn surgery which are carried out in two sequels. These include a proof that $0$-surgery characterizes infinitely many knots, generalizing results of Gabai from his 1987 resolution of the Property R Conjecture.
