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We describe the constructible derived category of sheaves on the $n$-sphere,stratified in a point and its complement, as a dg module category of a formaldg algebra. We prove formality by exploring two different methods: As acombinatorial approach, we reformulate the problem in terms of representationsof quivers and prove formality for the 2-sphere, for coefficients in aprincipal ideal domain. We give a suitable generalization of this formalityresult for the 2-sphere stratified in several points and their complement. As ageometric approach, we give a description of the underlying dg algebra in termsof differential forms, which allows us to prove formality for $n$-spheres, forreal or complex coefficients.

Formality of the constructible derived category for spheres: A combinatorial and a geometric approach