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The titular, foundational work of Beilinson not only gives a technique forgluing perverse sheaves but also implicitly contains constructions of thenearby and vanishing cycles functors of perverse sheaves. These constructionsare completely elementary and show that these functors preserve perversity andrespect Verdier duality on perverse sheaves. The work also defines a new,"maximal extension" functor, which is left mysterious aside from its role inthe gluing theorem. In these notes, we present the complete details of all ofthese constructions and theorems.

Notes on Beilinson's "How to glue perverse sheaves"