Aequationes Mathematicae, 73, no. 1-2 (2007), 71--77

A function from the group GL(2, R) to itself is called polynomial if it can be written as some product of constant functions, the identity function, and the function that maps every element to its inverse. We
give a necessary topological condition for a function to be polynomial. As a consequence we prove that transposition is not polynomial.