1997/07/01 by V. A. Vassiliev, Victor A. Vassiliev, Vassiliev, Victor A.
Computer Science · Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.AT #math.GT
paper · pdf · doi:10.48550/arxiv.math/9707212
arxiv created 1997/07/01 · openalex publication_date 1997/07/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a new method of computing cohomology groups of spaces of knots in \Rn, n ≥ 3, based on the topology of configuration spaces and two-connected graphs, and calculate all such classes of order ≤ 3. As a byproduct we define the higher indices, which invariants of knots in \R3 define at arbitrary singular knots. More generally, for any finite-order cohomology class of the space of knots we define its principal symbol, which lies in a cohomology group of a certain finite-dimensional configuration space and characterizes our class modulo the classes of smaller filtration.