The homotopy Conley index along heteroclinic
solutions of certain parabolic evolution equations is zero
under appropriate assumptions.
This result implies that the so-called connecting homomorphism
associated with a heteroclinic solution is an isomorphism. Hence, using Z-coefficients
it can be viewed as either 1 or −1 - depending on the choice of generators
for the homology Conley index. We develop a method to choose such generators,
and compute the connecting homomorphism
relative to these generators