论文标题
在三个球体中存在阳性双曲线轨道，并具有有限的自由组动作
Existence of a positive hyperbolic Reeb orbit in three spheres with finite free group actions
论文作者
论文摘要
令$（y，λ）$为非脱位触点三歧管。 D. Cristfaro-Gardiner, M. Hutshings and D. Pomerleano showed that if $c_{1}(ξ=\mathrm{Ker}λ)$ is torsion, then the Reeb vector field of $(Y,λ)$ has infinity many Reeb orbits otherwise $(Y,λ)$ is a lens space or three sphere with exaxtly two simple elliptic orbits.在同一篇论文中，他们还表明，如果$ b_ {1}（y）> 0 $，$（y，λ）$直接从Seiberg-witten Floer同源性和嵌入式接触同源性之间的异晶性中直接来自一个简单的阳性双曲线轨道。除此之外，他们询问带有Infinity的$（y，λ）$是否在$ b_ {1}（y）= 0 $下具有正值轨道。在本文中，我们在$ y \ y \ simeq s^{3} $下回答这个问题，具有非平凡有限的免费组动作，尤其是镜头空间$（l（p，q），λ），奇数$ p $作为$ s^{3} $的商空间。
Let $(Y,λ)$ be a non-degenerate contact three manifold. D. Cristfaro-Gardiner, M. Hutshings and D. Pomerleano showed that if $c_{1}(ξ=\mathrm{Ker}λ)$ is torsion, then the Reeb vector field of $(Y,λ)$ has infinity many Reeb orbits otherwise $(Y,λ)$ is a lens space or three sphere with exaxtly two simple elliptic orbits. In the same paper, they also showed that if $b_{1}(Y)>0$, $(Y,λ)$ has a simple positive hyperbolic orbit directly from the isomorhphism between Seiberg-Witten Floer homology and Embedded contact homology. In addition to this, they asked whether $(Y,λ)$ with infinity many simple orbits also has a positive hyperbolic orbit under $b_{1}(Y)=0$. In the present paper, we answer this question under $Y \simeq S^{3}$ with nontrivial finite free group actions, especially lens spaces $(L(p,q),λ)$ with odd $p$ as quotient spaces of $S^{3}$.
