奇瓦西里耶夫不变量在四圈处消失
Odd Vassiliev invariants vanish at four loops
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中文总结 AI 辅助
本文证明奇瓦西里耶夫猜想在四圈时成立，该猜想此前已被证明在1、2、3圈时成立，其核心是瓦西里耶夫不变量无法区分纽结与其逆，证明采用雅可比图等工具完成。
中文摘要 AI 辅助
奇瓦西里耶夫猜想断言，所有带奇数个腿的雅可比图在模AS和IHX关系下消失，等价于该猜想认为瓦西里耶夫不变量无法区分纽结与其逆。该猜想在1或2圈时是基础的，Moskovich和大月（Ohtsuki）已证明其在3圈时成立，本文证明其在4圈时成立。证明使用雅可比图、带多项式系数的权系统、可交换的带色腿以及若干消失准则。
英文摘要
The odd Vassiliev conjecture asserts that all Jacobi diagrams with an odd number of legs vanish modulo the AS and IHX relations. Equivalently, the conjecture asserts that Vassiliev invariants cannot distinguish a knot from its inverse. The conjecture is elementary for one 1 or 2 loops, and was proven by Moskovich and Ohtsuki for 3 loops. We establish the conjecture for 4 loops. Our proof uses Jacobi diagrams and weight systems with polynomial coefficients, commuting colored legs, and several vanishing criteria.
