Combinatorial formulas for cohomology of knot spaces
Combinatorial formulas for cohomology of knot spaces
复制标题
结空间上同调的组合公式
DOI：
10.17323/1609-4514-2001-1-1-91-123
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发表时间：
2001
影响因子：
0.8
通讯作者：
V. Vassiliev
中科院分区：
文献类型：
--
作者：
V. Vassiliev
我们发展了寻找R，n≥3中纽结空间的有限型上同调类的显式组合公式的方法，推广了R中纽结的不变量(即0维上同调类)的Polyak-Viro公式[9]。作为第一个应用，我们给出了3阶(约简mod 2)广义Teiblum-Turchin上循环(它是R↪→R中不可约为纽结不变量或其自然稳定化的最简单上同调类)的公式，以及作为推论，对紧纽结空间的所有1阶和2阶积分上同调类S↪→R在R.2000数学中，我们证明了所有这些上同调类在纽结空间中的非平凡性质。SUBJ。班级。主57M25、55R80；辅助57Q45、55T99、54F05。
We develop homological techniques for finding explicit combinatorial formulas for finite-type cohomology classes of spaces of knots in R, n ≥ 3, generalizing the Polyak—Viro formulas [9] for invariants (i.e., 0-dimensional cohomology classes) of knots in R. As the first applications, we give such formulas for the (reduced mod 2) generalized Teiblum—Turchin cocycle of order 3 (which is the simplest cohomology class of long knots R ↪→ R not reducible to knot invariants or their natural stabilizations), and for all integral cohomology classes of orders 1 and 2 of spaces of compact knots S ↪→ R. As a corollary, we prove the nontriviality of all these cohomology classes in spaces of knots in R. 2000 Math. Subj. Class. Primary 57M25, 55R80; Secondary 57Q45, 55T99, 54F05.