For a generalization of Morse-Bott functions on oriented surfaces, the homotopy type of the connected component of the identity in the stabilizer is completely described.
Codimension one foliatio ns with Bott-Morse singularities
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Homotopy type of stabilizers of smooth functions with non-isolated singularities on surfaces
For a generalization of Morse-Bott functions on oriented surfaces, the homotopy type of the connected component of the identity in the stabilizer is completely described.