Conformal Geometry of Discrete Groups and Manifolds
From Book News, Inc. Presents a systematic study of conformal geometry of n-manifolds, as well as its Riemannian counterparts (in particular, hyperbolic geometry). A unifying theme is the discrete holonomy groups of the corresponding geometric structures, which also involves algebra and dynamics. Topics covered include deformations of structures, Teichmuller spaces, discontinuous groups of homeomorphisms, geometrical finiteness, Kleinian manifolds, and uniformization. Apanasov (mathematics, U. of Oklahoma) does not pay much attention to 2-dimensional geometries covered by many classical and recent books, nor does he cover conformal geometries that appear at infinity for noncompact symmetric spaces with variable sectional curvature.Book News, Inc.®, Portland, OR
Synopsis This book presents a systematic account of conformal geometry of n-manifolds, as well as its Riemannian counterparts. A unifying theme is their discrete holonomy groups. In particular, hyperbolic manifolds, in dimension 3 and higher, are addressed. The treatment covers also relevant topology, algebra (including combinatorial group theory and varieties of group representations), arithmetic issues, and dynamics. Progress in these areas has been very fast sicne the 1980s, especially due to the...