Abstract
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 formal dg algebra. We prove formality by exploring two different methods. As a combinatorial approach, we reformulate the problem in terms of representations of quivers and prove formality for the 2-sphere, for coefficients in a principal ideal domain. We give a suitable generalization of this formality result for the 2-sphere stratified in several points and their complement. As a geometric approach, we give a description of the underlying dg algebra in terms of differential forms, which allows us to prove formality for n-spheres, for real or complex coefficients.
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Balthasar, A. Formality of the Constructible Derived Category for Spheres: A Combinatorial and a Geometric Approach. Mediterr. J. Math. 6, 403 (2009). https://doi.org/10.1007/s00009-009-0015-6
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DOI: https://doi.org/10.1007/s00009-009-0015-6