论文标题
{k} auffman支架多项式的类似物，用于不可方向表面的不可取向增厚
An analog of the {K}auffman bracket polynomial for knots in the non-orientable thickening of a non-orientable surface
论文作者
论文摘要
我们研究了不可取向表面的不可取向的增厚，特别是在不可定向的$ 3 $ 3 $ manifold（不可方向的表面）$ \ timple $ $ $ $ [0，1] $中。对于这些结，我们提出了Kauffman支架多项式的类似物。该多项式的构建密切反映了经典版本，在交叉符号的定义和交叉的正平滑迹象的定义上存在关键差异。我们证明该多项式是伪经典结的同位素不变，并证明它独立于经典的Kauffman支架在可定向的表面中的结中，这是不可考虑的不可方便表面的可定向双层盖。
We study pseudo-classical knots in the non-orientable thickening of a non-orientable surface, specifically knots that are orientation-preserving paths in a non-orientable $3$-manifold of the form (non-orientable surface) $\times$ $[0, 1]$. For these knots, we propose an analog of the Kauffman bracket polynomial. The construction of this polynomial closely mirrors the classical version, with key differences in the definitions of the sign of a crossing and the positive/negative smoothing of a crossing. We prove that this polynomial is an isotopy invariant of pseudo-classical knots and demonstrate that it is independent of the classical Kauffman bracket polynomial for knots in the thickened orientable surface, which is the orientable double cover of the non-orientable surface under consideration.
