论文标题
框架同源与一致性，ii
Framed instanton homology and concordance, II
论文作者
论文摘要
我们继续研究整数价值不变的$ν^\ sharp（k）$和$ r_0（k）$，共同确定了$ k $上所有非零dehn手术的框架Instanton同源性的尺寸。我们首先建立了一个“共轭”对称性，用于在我们较早的工作中构建的恢复图的分解，并用它来证明$ν^\ sharp（k）$始终是零或奇数。然后，我们将这些技术结果应用于同源性共同体小组中的线性独立性，以定义HOM的$ε$ invariant在Heegaard Floer同源性中的Instanton flo sublogue $ε^\ sharp（k）$，并以$ s^3 $^$^3 $ n n ne ne n n o ny n o ny te n s ny n n n n of s n of heegaard floer同源性。
We continue our study of the integer-valued knot invariants $ν^\sharp(K)$ and $r_0(K)$, which together determine the dimensions of the framed instanton homologies of all nonzero Dehn surgeries on $K$. We first establish a "conjugation" symmetry for the decomposition of cobordism maps constructed in our earlier work, and use this to prove, among many other things, that $ν^\sharp(K)$ is always either zero or odd. We then apply these technical results to study linear independence in the homology cobordism group, to define an instanton Floer analogue $ε^\sharp(K)$ of Hom's $ε$-invariant in Heegaard Floer homology, and to the problem of characterizing a given 3-manifold as Dehn surgery on a knot in $S^3$.
