论文标题
固体圆环中的结空间，在增厚的圆环中的结，并在3杆中链接
Spaces of knots in the solid torus, knots in the thickened torus, and links in the 3-sphere
论文作者
论文摘要
我们递归地确定了3个球体旋转中任何不可还原框架链路的空间的同喻类型。这使我们进入了固体圆环中任何结空间的同质类型，从而回答了阿诺德提出的一个问题。我们类似地研究了三个球体，模量旋转和增厚圆环中的结空间中的无框连接的空间。子午旋转的亚组分裂为除UNENGNOT外，任何框架链路的基本组的直接因素。它的发电机可以看作是在长结空间中的Gramain循环的概括。通过某些此类旋转来实现商，这与我们研究的空间有关。我们所有的结果都概括了Hatcher和Budney先前的工作。我们提供了许多例子，并明确描述了基本群体的发电机。
We recursively determine the homotopy type of the space of any irreducible framed link in the 3-sphere, modulo rotations. This leads us to the homotopy type of the space of any knot in the solid torus, thus answering a question posed by Arnold. We similarly study spaces of unframed links in the 3-sphere, modulo rotations, and spaces of knots in the thickened torus. The subgroup of meridional rotations splits as a direct factor of the fundamental group of the space of any framed link except the unknot. Its generators can be viewed as generalizations of the Gramain loop in the space of long knots. Taking the quotient by certain such rotations relates the spaces we study. All of our results generalize previous work of Hatcher and Budney. We provide many examples and explicitly describe generators of fundamental groups.
