TOPOLOGY OF TWO-CONNECTED GRAPHS AND HOMOLOGY OF SPACES OF KNOTS

VICTOR A. VASSILIEV

Abstract. We propose a new method of computing cohomology groups of spaces of knots in ℝ^{n}, n ≥ 3, based on the topology of configuration spaces and twoconnected graphs, and calculate all such classes of order ≤ 3. As a byproduct we define the higher indices, which invariants of knots in ^{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 finitedimensional configuration space and characterizes our class modulo the classes of smaller filtration.