%0 Journal Article %T $\mathbb P$-objects and autoequivalences of derived categories %A D. Huybrechts %A R. P. Thomas %J Mathematics %D 2005 %I arXiv %X We describe new autoequivalences of derived categories of coherent sheaves arising from what we call $\mathbb P^n$-objects of the category. Standard examples arise from holomorphic symplectic manifolds. Under mirror symmetry these autoequivalences should be mirror to Seidel's Dehn twists about lagrangian $\mathbb P^n$ submanifolds. We give various connections to spherical objects and spherical twists, and include a simple description of Atiyah and Kodaira-Spencer classes in an appendix. %U http://arxiv.org/abs/math/0507040v2