Matroid theory and Chern-Simons

It is shown that matroid theory may provide a natural mathematical framewor k for a duality symmetries not only for quantum Yang-Mills physics, but als o for M-theory. Our discussion is focused in an action consisting purely of the Chern-Simons term, but in principle the main ideas can be applied beyo nd such an action. In our treatment the theorem due to Thistlethwaite, whic h gives a relationship between the Tutte polynomial for graphs and Jones po lynomial for alternating knots and links, plays a central role. Before addr essing this question we briefly mention some important aspects of matroid t heory and we point out a connection between the Fano matroid and D=11 super gravity. Our approach also seems to be related to loop solutions of quantum gravity based in an Ashtekar formalism. (C) 2000 American Institute of Phy sics. [S0022-2488(00)00712-X].