On the equivalence of Legendrian and transverse invariants in knot Floer homology
On the equivalence of Legendrian and transverse invariants in knot Floer homology
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结Floer同调中Legendrian和横向不变量的等价性
DOI：
10.2140/gt.2013.17.925
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发表时间：
2011
影响因子：
2
通讯作者：
Vera Vértesi
中科院分区：
文献类型：
--
作者：
John A. Baldwin;D. Vela;Vera Vértesi
Ozsvath、Szabo和Thurston利用纽结Floer同调的网格图公式，定义了紧接触三维球面中横结的不变量。不久之后，Lisca，Ozsvath，Stipsicz和Szabo使用开卷分解定义了任意切触三维流形中横结的不变量。已经证明，这些不变量在它们都被定义的地方是一致的。我们证明了这一事实，通过定义另一个不变量的横结，表明这第三个不变量同意上述两个。57 M27; 57 R58
Using the grid diagram formulation of knot Floer homology, Ozsvath, Szabo and Thurston defined an invariant of transverse knots in the tight contact 3‐sphere. Shortly afterwards, Lisca, Ozsvath, Stipsicz and Szabo defined an invariant of transverse knots in arbitrary contact 3‐manifolds using open book decompositions. It has been conjectured that these invariants agree where they are both defined. We prove this fact by defining yet another invariant of transverse knots, showing that this third invariant agrees with the two mentioned above. 57M27; 57R58