Let $f $ be a Morse function on a smooth compact surface $M$ and $\mathcal{S}'(f)$ be a group of $f$-preserving diffeomorphisms of $M$ which are isotopic to the identity map. Let also $G(f)$ be a group of automorphisms of the graph of $f$ induced by elements from $\mathcal{S}'(f)$, and $\Delta'$ be a subgroup of $\mathcal{S}'(f)$ of diffeomorphisms which trivially act on the graph of $f$ and are isotopic to the identity map... (read more)

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