• action
• algebraic geometry
• braid groups
• category
• derived categories
• DG-algebra
• homological algebra
• mapping class group
• topology

The aim of this thesis is to explain the construction of the ``spherical twists'' invented by P. Seidel and R. Thomas. After defining ``spherical objects'' in the bounded derived category of a fairly general $k$-linear category, we will define the ``spherical twist'' associated to it and study its main property: in particular, this produces an exact autoequivalence of the derived category. If a sequence of spherical objects satisfies some ``adjacency condition'', then their spherical twist satisfy the braid relations, thus one can define an action of some braid group $\Br_{m+1}$ on such derived categories. It is a non-trivial fact that this action is faithful: in order to work out the proof, a consistent amount of techniques from differential graded algebra are discussed.