AI 中文总结
该研究利用基于模2瞬子同调的Froyshov不变量$q_3$，证明存在Dehn手术数可任意大的双曲整数同调球，并将相关不等式扩展至有理同调球。
AI 中文摘要
我们证明存在双曲整数同调球，其Dehn手术数可任意大。此前，尚无整数同调球被知晓具有大于2的手术数。我们的方法利用整数同调球的Froyshov不变量$q_3$，该不变量基于模2瞬子同调定义。我们证明，若$W: Y \to Y'$是整数同调球间的配边，且其一阶同调中无2-挠，则$-b^+(W) \leq q_3(Y') - q_3(Y) \leq b^-(W)$。我们还将$q_3$及该不等式扩展至有理同调球。
英文摘要
We prove that there exist hyperbolic integer homology spheres with arbitrarily large Dehn surgery number. Previously, no integer homology sphere was known to have a surgery number larger than $2$. Our approach uses Froyshov's invariant $q_3$ of integer homology spheres, which is defined in terms of mod 2 instanton homology. We show that if $W: Y \to Y'$ is a cobordism between integer homology spheres with no $2$-torsion in its first homology, then $-b^+(W) \le q_3(Y') - q_3(Y) \le b^-(W)$. We also extend both $q_3$ and the inequality to rational homology spheres.
Comments67 pages, 2 figures, comments welcome
