Cutting planes and the elementary closure in fixed dimension

the situation is different if the number of variables is fixed. For
this, Lenstra (1983) gave a polynomial algorithm.
A prominent way to attack an integer programming problem is the
cutting plane method due to Gomory (1958). We prove that the cutting
plane closure operation is a "polynomial concept" in fixed
dimension. Previous known bounds on the complexity of the cutting
plane closure due to so-called TDI systems are exponential in fixed
dimension.
Finally we present an algorithm that computes cutting planes from
this polynomial description of the cutting plane closure $P'$ of
$P$.

Joint work with Alexander Bockmayr, Loria, France