Continuation maps give functorial morphisms between Morse fundamental groups, including on different manifolds via grafted trajectories, and the Morse fundamental group of an interpolation function on M×R is a relative fundamental group.
We have a unique critical point ats = 0, which happens to be a minimum, and its limits at±∞ are +∞ (in particular, it is decreasing befores = 0, and increasing after)
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Continuation maps for the Morse fundamental group
Continuation maps give functorial morphisms between Morse fundamental groups, including on different manifolds via grafted trajectories, and the Morse fundamental group of an interpolation function on M×R is a relative fundamental group.