| 韩友发,梁良,王树新,孔令天.某些链环和三维流形不变量的计算[J].数学年刊A辑,2025,46(4):449~464 |
| 某些链环和三维流形不变量的计算 |
| The Calculation of Invariants for Some Links and 3-Manifolds |
| 投稿时间：2025-02-08 修订日期：2025-12-25 |
| DOI：10.16205/j.cnki.cama.2025.0028 |
| 中文关键词: 三维流形不变量 广义标架链环 广义树状链环 |
| 英文关键词:Invariants for 3-manifold Generalized framed links Generalized tree |
| 基金项目:国家自然科学基金(No. 12526404)；辽宁省自然科学基金(No. 20250101)；大连市科技创新基金(No. LJ212410165006) |
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| 中文摘要: |
| 该文主要研究某些具体类链环确定的三维流形不变量的计算。设$M_L$是$S^3$中沿着标架链环$(L, f)$进行手术后得到的可定向三维流形，对于标架链环进行同痕、$K_+$和$K_-$变换后得到了链环不变量，进而得到三维流形$M_L$的不变量。给出了某类广义树状链环$T_G$和链环$L_G$确定的Blanchet型三维流形不变量的计算公式，为进一步研究由链环理论得到的三维流形不变量提供了若干方法和视角。 |
| 英文摘要: |
| This paper mainly analyzes the calculation of invariants for 3-manifold defined by some links. Suppose $M_L$ represents the orientable 3-manifold obtained by surgery on $S^3$ along the framed link ( $(L, f)$ ), the authors get the link invariant after isotopy, $K_+$ move and $K_-$ move for the framed link. Then the invariants of 3-manifold $M_L$ are obtained. This paper studies the two calculated formulas of Blanchet shaped invariants for 3-manifold defined by certain generalized tree links $T_G$ and links $L_G$ , provides several methodologies and perspectives for the further study of 3-manifold invariants derived from link theory. |
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