论文标题
飞行定理的几何证明
A geometric proof of the flyping theorem
论文作者
论文摘要
1898年，泰特（Tait）断言了交替结图的几种特性。这些断言被称为泰特的猜想，并一直开放，直到1985年琼斯多项式发现。新的多项式不变性很快就证明了泰特所有的猜想，并于1993年与Menasco-Menasco-Thisterthwaite-Thistlethwaite证明了Tait的Tait Flyping猜想。 2017年，格林（和独立的豪伊）通过以几何链接来表征福克斯的长期问题。然后，格林利用他的特征给出了第一个{\ it几何}的一部分猜想的证明。我们使用Greene的特征，Menasco的交叉结构，以及同位素和{\ IT重新置换}的层次结构，以给出了Menasco-thistlethwaite的第一个几何证据，即Thistlethwaite的fly fly定理。
In 1898, Tait asserted several properties of alternating knot diagrams. These assertions became known as Tait's conjectures and remained open until the discovery of the Jones polynomial in 1985. The new polynomial invariants soon led to proofs of all of Tait's conjectures, culminating in 1993 with Menasco--Thistlethwaite's proof of Tait's flyping conjecture. In 2017, Greene (and independently Howie) answered a longstanding question of Fox by characterizing alternating links geometrically. Greene then used his characterization to give the first {\it geometric} proof of part of Tait's conjectures. We use Greene's characterization, Menasco's crossing ball structures, and a hierarchy of isotopy and {\it re-plumbing} moves to give the first entirely geometric proof of Menasco--Thistlethwaite's flyping theorem.
