Many of the original research and survey monographs in pure and been groundbreaking and have come to be regarded as foundational to the subject. Through the MBC Series, a select number of these modern classics, entirely uncorrected, are being re-released in accessible to new generations of students, scholars, and researchers. paperback (and as eBooks) to ensure that these treasures remain applied mathematics published by Birkhäuser in recent decades have

We study the symplectic geometry of moduli spaces M r of polygons with fixed side lengths in Euclidean space. We show that M r has a natural structure of a complex analytic space and is complex-analytically isomorphic to the weighted quotient of (5 2 ) n by PLS(2,C) constructed by Deligne and Mostow. We study the Hamiltonian flows on M r obtained by bending the polygon along diagonals and show the group generated by such flows acts transitively on M r . We also relate these flows to the twist flows of Goldman and Jeffrey-Weitsman.

Let θ : π 1 (R) → PSL(2, C) be a homomorphism of the fundamental group of an oriented, closed surface R of genus exceeding one. We will establish the following theorem.Theorem. Necessary and sufficient for θ to be the monodromy representation associated with a complex projective stucture on R, either unbranched or with a single branch point of order 2, is that θ(π 1 (R)) be nonelementary. A branch point is required if and only if the representation θ does not lift to SL(2, C).

We study the topology of moduli spaces of polygons with fixed side lengths in the Euclidean plane. We establish a duality between the spaces of marked Euclidean polygons with fixed side lengths and marked convex Euclidean polygons with prescribed angles.

Special aspects of infinite or finite groups-Geometric group theory. msc | Group theory and generalizations-Special aspects of infinite or finite groups-Hyperbolic groups and nonpositively curved groups. msc | Group theory and generalizations-Special aspects of infinite or finite groups-Asymptotic properties of groups. msc | Group theory and generalizations-Special aspects of infinite or finite groups-Generators, relations, and presentations. msc | Group theory and generalizations-Special aspects of infinite or finite groups-Solvable groups, supersolvable groups. msc | Group theory and generalizations-Special aspects of infinite or finite groups-Nilpotent groups. msc | Group theory and generalizations-Special aspects of infinite or finite groups-Fundamental groups and their automorphisms. msc | Group theory and generalizations-Structure and classification of infinite or finite groups-Groups acting on trees. msc | Group theory and generalizations-Structure and classification of infinite or finite groups-Residual properties and generalizations; residually finite groups. msc | Manifolds and cell complexes-Low-dimensional topology-Topological methods in group theory. msc