Background
The authors note that (1) Petit et al. (1999) concluded that the decline in atmospheric CO2 concentration lagged the decline in air temperature at the onset of the four glacial epochs that are evident in the Vostok ice core data, (2) Fischer et al. (1999) concluded that the increase in atmospheric CO2 concentration lagged the increase in air temperature at the onset of interglacial warmth in the same data set, and (3) Caillon et al. (2003) concluded that for the period 230-250 ka BP (approximately corresponding to Glacial Termination III), temperature variations also led variations in greenhouse gas concentration (GGC).

What was done
To quantitatively check these several conclusions, Vakulenko et al. say they calculated "cross correlations of the average temperature (based on the deuterium dD content) and GGC variations estimated for all glacial cycles in the Vostok ice core" by means of a wavelet transform technique.

What was learned
It was determined, in the words of the Russian scientists, that "all four warm periods in the Vostok core record in fact began with the temperature growth," and that "both the beginning and termination of GGC growth always demonstrated a lag relative to the warming-cooling replacement episode," leading them to conclude that "GGC variations followed rather than anticipated temperature variations during the critical episodes of the glacial cycle."

What it means
In the final paragraph of their paper, and after stating that "temperature variations always preceded GGC variations during the four main glacial cycles recorded in the Vostok ice core," Vakulenko et al. state that "of particular importance is the fact that the temperature began to decrease after reaching a very high value, although the GGC values continued to increase."  Hence, they end their paper with a provocative question: "Will we witness cooling in the near future, even though anthropogenic GGC will continue to increase?"  At the present, one can only wonder; for the data from four glacial-interglacial cycles demonstrate that the speculation cannot be rejected out of hand.  In fact, our review of the paper of Damon and Laut (2004) suggests that this scenario may actually be in process of occurring right now, if it is indeed true that post-Little Ice Age warming truly peaked in the late 1930s and early 1940s, as many data sets clearly indicate it did.

References
Caillon, N., Severinghaus, J.P., Jouzel, J., Barnola, J.-M., Kang, J. and Lipenkov, V.Y.  2003.  Timing of atmospheric CO2 and Antarctic temperature changes across Termination III.  Science 299: 1728-1731.

Damon, P.E. and Laut, P.  2004.  Pattern of strange errors plagues solar activity and terrestrial climatic data.  EOS, Transactions, American Geophysical Union 85: 370, 374

Fischer, H., Wahlen, M., Smith, J., Mastroianni, D. and Deck B.  1999.  Ice core records of atmospheric CO2 around the last three glacial terminations.  Science 283: 1712-1714.

Petit, J.R., Jouzel, J., Raynaud, D., Barkov, N.I., Barnola, J.-M., Basile, I., Bender, M., Chappellaz, J., Davis, M., Delaygue, G., Delmotte, M., Kotlyakov, V.M., Legrand, M., Lipenkov, V.Y., Lorius, C., Pepin, L., Ritz, C., Saltzman, E., and Stievenard, M.  1999.  Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica.  Nature 399: 429-436.