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The paper describes a natural splitting in the rational homology and homotopyof the spaces of long knots. This decomposition presumably arises from thecabling maps in the same way as a natural decomposition in the homology of loopspaces arises from power maps. The generating function for the Eulercharacteristics of the terms of this splitting is presented. Based on thisgenerating function we show that both the homology and homotopy ranks of thespaces in question grow at least exponentially. Using natural graph-complexeswe show that this splitting on the level of the bialgebra of chord diagrams isexactly the splitting defined earlier by Dr. Bar-Natan. In the Appendix wepresent tables of computer calculations of the Euler characteristics. Thesecomputations give a certain optimism that the Vassiliev invariants of order >20 can distinguish knots from their inverses.

Hodge decomposition in the homology of long knots