论文标题
Instanton Floer同源性的结节手术公式II：应用
Knot surgery formulae for instanton Floer homology II: applications
论文作者
论文摘要
这是作者早期作品的同伴论文，该论文证明了框架同源性的整体手术公式。首先，我们提出了大型手术配方的增强，这是任何3个manifold中无原样结的合理手术公式，以及编码$ i^\ sharp（s^3_0（k））$的大部分的公式。其次，我们使用积分手术公式来研究许多3个序列的框架激体同源性：塞弗特的纤维纤维空间，具有非零的孔属度，尤其是在任何可定位的表面上的非平凡圆圈捆绑包，在一个交替的打结家族上进行手术，并带有扭曲的白头双打和剪接，并带有Twist Twist Knots。最后，我们使用以前的技术和计算来研究几乎L-space结，$ {\ it i.e。} $，带$ k \ subset s^3 $带有$ \ dim i^\ sharp（s_n^3（k））= n+2 $，用于某些$ n \ in \ in \ mathbb {n} n} _____+$。我们表明，几乎L空间结的属至少$ 2 $是纤维纤维和强烈的准阳性，并且一个几乎是L-Space结的属必须是Rolfsen的结台中的$ 8或$ 5_2 $结的镜子。
This is a companion paper to earlier work of the authors, which proved an integral surgery formula for framed instanton homology. First, we present an enhancement of the large surgery formula, a rational surgery formula for null-homologous knots in any 3-manifold, and a formula encoding a large portion of $I^\sharp(S^3_0(K))$. Second, we use the integral surgery formula to study the framed instanton homology of many 3-manifolds: Seifert fibered spaces with nonzero orbifold degrees, especially nontrivial circle bundles over any orientable surface, surgeries on a family of alternating knots and all twisted Whitehead doubles, and splicings with twist knots. Finally, we use the previous techniques and computations to study almost L-space knots, ${\it i.e.}$, the knots $K\subset S^3$ with $\dim I^\sharp(S_n^3(K))=n+2$ for some $n\in\mathbb{N}_+$. We show that an almost L-space knot of genus at least $2$ is fibered and strongly quasi-positive, and a genus-one almost L-space knot must be either the figure eight or the mirror of the $5_2$ knot in Rolfsen's knot table.
