论文标题
同源协调和无限等级的免费亚组
Homology concordance and an infinite rank free subgroup
论文作者
论文摘要
如果同源性在同源性的恢复中平稳地一致，则两个结是同源性的。组$ \ hat {\ Mathcal {c}} _ {\ Mathbb {z}} $（tesp。$ \ Mathcal {c} _ {\ Mathbb {z}} $）以前定义为同源性领域中的结节集合（bamerology homology balls balls HON HOMOLOLOGY BALLS（usporly）（proves）$ s poss.s s^3 $ s^3 $。我们证明$ \ hat {\ Mathcal {C}} _ {\ Mathbb {Z}} / \ MathCal {C} _ {\ Mathbb {Z}} $包含一个$ \ MATHBB {Z}我们通过将过滤的映射锥公式应用于$ L $ - 太空结，并在连接的结综合体的帮助下证明了线性独立性，来构建我们的示例家庭。
Two knots are homology concordant if they are smoothly concordant in a homology cobordism. The group $\hat{\mathcal{C}}_{\mathbb{Z}}$ (resp. $\mathcal{C}_{\mathbb{Z}}$) was previously defined as the set of knots in homology spheres that bounds homology balls (resp. in $S^3$), modulo homology concordance. We prove $\hat{\mathcal{C}}_{\mathbb{Z}} / \mathcal{C}_{\mathbb{Z}}$ contains a $\mathbb{Z}^{\infty}$ subgroup. We construct our family of examples by applying the filtered mapping cone formula to $L$--space knots, and prove linear independence with the help of the connected knot complex.
