By Benson Farb

The looks of mapping type teams in arithmetic is ubiquitous. The ebook provides 23 papers containing difficulties approximately mapping category teams, the moduli house of Riemann surfaces, Teichm??ller geometry, and similar parts. every one paper focusses thoroughly on open difficulties and instructions. the issues diversity in scope from particular computations, to extensive courses. The objective is to have a wealthy resource of difficulties that have been formulated explicitly and accessibly. The e-book is split into 4 elements. half I comprises difficulties at the combinatorial and (co)homological group-theoretic points of mapping type teams, and how during which those relate to difficulties in geometry and topology. half II concentrates on connections with category difficulties in 3-manifold thought, the speculation of symplectic 4-manifolds, and algebraic geometry. a large choice of difficulties, from realizing billiard trajectories to the class of Kleinian teams, will be diminished to differential and artificial geometry difficulties approximately moduli house. Such difficulties and connections are mentioned partially III. Mapping category teams are similar, either concretely and philosophically, to a couple of different teams, reminiscent of braid teams, lattices in semisimple Lie teams, and automorphism teams of unfastened teams. half IV concentrates on difficulties surrounding those relationships. This e-book will be of curiosity to an individual learning geometry, topology, algebraic geometry or endless teams. it truly is intended to supply concept for everybody from graduate scholars to senior researchers.