  In this paper we study twisted complexes on a ringed space and prove that it
gives a new dg-enhancement of the derived category of perfect complexes on that
space. A twisted complex is a collection of locally defined sheaves together
with the homotopic gluing data. In this paper we construct a dg-functor from
twisted complexes to perfect complexes, which turns out to be a dg-enhancement.
This new enhancement has the advantage of being completely geometric and it
comes directly from the definition of perfect complex . In addition we will
talk about some applications and further topics around twisted complexes.
