Conley index orientations

Axel Jänig

Abstract


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 $\mathbb{Z}$-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.

Keywords


Conley index theory; Morse decompositions; reaction diffusion equations

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