Topology of two-connected graphs and homology of spaces of knots

Victor A. Vassiliev

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arXiv · math/9707212

Topology of two-connected graphs and homology of spaces of knots

Victor A. Vassiliev

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Abstract

We propose a new method of computing cohomology groups of spaces of knots in $\R^n$, $n \ge 3$, based on the topology of configuration spaces and two-connected graphs, and calculate all such classes of order $\le 3.$ As a byproduct we define the higher indices, which invariants of knots in $\R^3$ 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.

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BibTeX RIS

Victor A. Vassiliev. 1997-07-01. Topology of two-connected graphs and homology of spaces of knots. https://arxiv.org/abs/math/9707212

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