# the intersection number between a trivial loop and a meridian in the torus

#### student2011

Let A and B be two closed curves intersect on the torus transversally at a point, the intersection index of the crossing point is defined to be positive if the tangent vectors to A and B form an oriented basis for the tangent plane of the torus and negative otherwise. Then the intersection number of A and B is the sum of the signs over all intersection points between A and B. The intersection number of two classes in the homology is the minimum intersection number over all representatives the two classes.

Suppose A is a trivial loop ( boundary of a disk) in the torus and B is a meridian of the torus. Suppose also that A and B intersect at two crossing points, then what is the intersection number of A and B in this case? Can we have such a case? I am confusing because the orientation of basis of tangent vectors is preserved along the trivial loop A in the torus, so we can not have positive and negative orientations at the transversal intersection points, is this true? Any guidance or comments is highly appreciated