I am reading a paper (Gutel et al., J. Mater. Chem. 2007, 17, 3290-3292) and I have come across the following reaction:
In organic solvents, the decomposition under mild conditions of ($\eta^4$-1,5-cyclooctadiene)($\eta^6$-1,3,5-cyclooctatriene)ruthenium(0), Ru(COD)(COT), under a dihydrogen atmosphere gives ruthenium nanoparticles (RuNPs), by releasing cyclooctane (COA).
$$\text{Ru(COD)(COT)} + \text{H}_2 \rightarrow \text{RuNPs} + \text{COA}$$
What do the $\eta^4$ and $\eta^6$ notations represent? Do they somehow specify the coordination "connectivity" of the Ru(0) and the COD and COT coordinating ligands?
Below, I have drawn the (two-dimensional) structures of COD and COT. How would I draw the connectivity of Ru(COD)(COT), or is it not specified in the given name?

