Using carbon dioxide the chemical formula often given for carbon
fixation is...
6CO2 + 12H2O - C6H12O6 + 6O2 + 6H20

but in principle, carbon monoxide could be used as follows:

6CO + 12H2O -C6H12O6 + 3O2 + 6H2O

I know the Calvin process is complicated and involves many intermediate
steps (and these intermediate steps may be impossible with CO).

My question: Has any research been done involving plants in an
atmosphere of CO? Or has the assumption been made that it just won't
work?

Thanks.