  We find lower bounds on the number of intersection points between two
relatively exact Hamiltonian isotopic Lagrangians. The bounds are given in
terms of the cuplength of the Lagrangian in various multiplicative generalised
cohomology theories. The intersection of the Lagrangians need not be
transverse, however, we require certain orientation assumptions. This gives
stronger bounds than previous estimates on the number of self-intersection
points of a suitable closed, relatively exact Lagrangian diffeomorphic to
Sp$(2)$ or Sp$(3)$. Our proof uses Lusternik-Schnirelmann theory, following and
extending work by Hofer.
