论文标题
具有完美圆值摩尔斯功能的双曲线4个manifolds
Hyperbolic 4-manifolds with perfect circle-valued Morse functions
论文作者
论文摘要
我们展示了具有完美圆值的摩尔斯函数（即圆值摩尔斯函数$ f \ colon m \ to S^1 $，只有index 2关键点，我们都具有完美的圆值摩尔斯函数（即圆值摩尔斯函数$ f \ colon Morse函数），它具有一些（紧凑和cus量）有限体积的双曲线四个manifolds m。我们特别构建了一个示例，其中每个通用圆值函数都适合完美的函数。 直接的后果是存在无限的许多有限体积（紧凑型和cus）双曲线4个manifolds $ m $，其手柄分解为1和3个手柄，因此具有有限的betti betti数字$ b_1（m）$，$ b_3（m）$，$ b_3（m）$，等级$ $π_1（m）$（m）$。
We exhibit some (compact and cusped) finite-volume hyperbolic four-manifolds M with perfect circle-valued Morse functions, that is circle-valued Morse functions $f\colon M \to S^1$ with only index 2 critical points. We construct in particular one example where every generic circle-valued function is homotopic to a perfect one. An immediate consequence is the existence of infinitely many finite-volume (compact and cusped) hyperbolic 4-manifolds $M$ having a handle decomposition with bounded numbers of 1- and 3-handles, so with bounded Betti numbers $b_1(M)$, $b_3(M)$ and rank of $π_1(M)$.
