By Benson Farb

ISBN-10: 0821838385

ISBN-13: 9780821838389

The looks of mapping classification teams in arithmetic is ubiquitous. The publication provides 23 papers containing difficulties approximately mapping type teams, the moduli area of Riemann surfaces, Teichm??ller geometry, and comparable components. every one paper focusses thoroughly on open difficulties and instructions. the issues diversity in scope from particular computations, to vast courses. The objective is to have a wealthy resource of difficulties which were formulated explicitly and accessibly. The e-book is split into 4 components. half I comprises difficulties at the combinatorial and (co)homological group-theoretic points of mapping category teams, and how within which those relate to difficulties in geometry and topology. half II concentrates on connections with class difficulties in 3-manifold idea, the speculation of symplectic 4-manifolds, and algebraic geometry. a wide selection of difficulties, from realizing billiard trajectories to the type of Kleinian teams, will be lowered to differential and artificial geometry difficulties approximately moduli area. Such difficulties and connections are mentioned partially III. Mapping type teams are comparable, either concretely and philosophically, to a few different teams, similar to braid teams, lattices in semisimple Lie teams, and automorphism teams of unfastened teams. half IV concentrates on difficulties surrounding those relationships. This ebook might be of curiosity to somebody learning geometry, topology, algebraic geometry or countless teams. it really is intended to supply idea for everybody from graduate scholars to senior researchers.