论文标题
透镜空间上极地摩尔斯 - 摩托叶叶的差异类的同喻类型，1
Homotopy types of diffeomorphism groups of polar Morse-Bott foliations on lens spaces, 1
论文作者
论文摘要
令$ t = s^1 \ times d^2 $为坚固的圆环，$ \ nathcal {f} $ $ t $上的莫尔斯 - 荷兰特叶子与$ 2 $ -tori平行于边界平行于边界，一个单一的圆圈$ s^1 \ times 0 $，这是torus $ t $的中心圈子，以及$ \ nathcal {$ d d} $ cal cal call cal $ t $固定在$ \ partial t $上的$ t $的差异性，并留下叶子$ \ mathcal {f} $不变的每个叶子。我们证明$ \ MATHCAL {D}（\ Mathcal {f}，\ partial t）$是合可能的。 通过它们的边界之间的某些差异性，我们将获得镜头空间$ l_ {p，q} $的两份$ t副本，并使用Morse-Bott Foliation $ \ Mathcal {f} _ {p，q} $从$ \ nathcal {f} $上获得的$ t $ of $ t $。我们还计算了$ \ MATHCAL {D}的同质类型（\ Mathcal {f} _ {p，q}）$ $ l_ {p，q} $的diffeoMorthisms $，留下$ \ mathcal {f} _ {p，q，q，q，q} $不变的每个叶子。
Let $T= S^1\times D^2$ be the solid torus, $\mathcal{F}$ the Morse-Bott foliation on $T$ into $2$-tori parallel to the boundary and one singular circle $S^1\times 0$, which is the central circle of the torus $T$, and $\mathcal{D}(\mathcal{F},\partial T)$ the group of diffeomorphisms of $T$ fixed on $\partial T$ and leaving each leaf of the foliation $\mathcal{F}$ invariant. We prove that $\mathcal{D}(\mathcal{F},\partial T)$ is contractible. Gluing two copies of $T$ by some diffeomorphism between their boundaries, we will get a lens space $L_{p,q}$ with a Morse-Bott foliation $\mathcal{F}_{p,q}$ obtained from $\mathcal{F}$ on each copy of $T$. We also compute the homotopy type of the group $\mathcal{D}(\mathcal{F}_{p,q})$ of diffeomorphisms of $L_{p,q}$ leaving invariant each leaf of $\mathcal{F}_{p,q}$.
