论文标题
在结零外科同态的内核上
On the kernel of the zero-surgery homomorphism from knot concordance
论文作者
论文摘要
Kawauchi在同源性$ s^1 $ s $ s $$ s^2 $下定义了一个组结构，称为$ \ widetilde {h} $ - cobordism。该组通过零手术的操作给出了结一致性组的同态。自然要问零外科同态是否具有侵入性。我们表明，这个问题在平滑类别中具有负面答案。确实，使用从结浮子同源性得出的结结一致性不变性，我们表明零手术同构的核包含$ \ mathbb {z}^\ infty $ -subgroup。
Kawauchi defined a group structure on the set of homology $S^1$$\times$$S^2$'s under an equivalence relation called $\widetilde{H}$-cobordism. This group receives a homomorphism from the knot concordance group, given by the operation of zero-surgery. It is natural to ask whether the zero-surgery homomorphism is injective. We show that this question has a negative answer in the smooth category. Indeed, using knot concordance invariants derived from knot Floer homology we show that the kernel of the zero-surgery homomorphism contains a $\mathbb{Z}^\infty$-subgroup.
