论文标题
紧密联系$ 3 $ manifolds的联络人形态组的同型类型，第一部分
The homotopy type of the contactomorphism groups of tight contact $3$-manifolds, part I
论文作者
论文摘要
我们计算带有Legendrian边界嵌入磁盘嵌入空间的同质类型，每当thurston-bennequin不变性的旋转数量的绝对价值的总和为$ -1 $，证明它与平滑嵌入的太空相等，thurston-bennequin不变性是$ -1时，使用相同的想法，还确定了凸球嵌入空间的同副率类型，就光滑球体的空间而言，将凸球嵌入到一个紧密的$ 3 $倍中。结果，我们确定了长传说中的un开口空间的同质类型，满足了先前的条件，并将其成3美元的紧密折叠，以及长横向解开的空间，并以自连接数字$ -1 $ -1 $ $ -1 $，证明这些空间是同质的，等于平稳的Unknots。我们还确定了每个普遍紧密的手柄，标准$ \ ns^1 \ times \ ns^2 $的接触型类型的同型类型，以及在具有非空边界的紧凑型表面上的每一个legendrian纤维，部分解决了由于E. giroux而引起的猜想。最后，我们表明Legendrian $（n，n）$ - 与最大的Thurston-Bennequin不变式链接的嵌入空间相当于$ \ u（2）\ times k（\ times k（\ nathcal {m} _n，1）$ $ n $ - 孔。
We compute the homotopy type of the space of embeddings of convex disks with Legendrian boundary into a tight contact $3$-manifold, whenever the sum of the absolute value of the rotation number of the boundary with the Thurston-Bennequin invariant is $-1$, proving that it is homotopy equivalent to the space of smooth embeddings. Using the same ideas it is also determined the homotopy type of the space of embeddings of convex spheres into a tight $3$-fold in terms of the space of smooth spheres. As a consequence we determine the homotopy type of the space of long Legendrian unknots, satisfying the previous condition, into a tight $3$-fold and also of the space of long transverse unknots with self-linking number $-1$, proving that these spaces are homotopy equivalent to the space of smooth long unknots. We also determine the homotopy type of the contactomorphism group of every universally tight handlebody, the standard $\NS^1\times\NS^2$ and every Legendrian fibration over a compact orientable surface with non-empty boundary, partially solving a conjecture due to E. Giroux. Finally, we show that the space of embeddings of Legendrian $(n,n)$-torus links with maximal Thurston-Bennequin invariant is homotopy equivalent to $\U(2)\times K(\mathcal{M}_n,1)$, where $\mathcal{M}_n$ is the mapping class group of the $2$-sphere with $n$-holes.
