Conformal Geometry Of Discrete Groups And Manifolds (de Gruyter Expositions In Mathematics,)
by B. N. Apanasov /
2000 / English / DjVu
11.3 MB Download
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 Thurston geometrization
program, leading to the solution of many difficult problems. A
strong effort has been made to point out new connections and
perspectives in the field and to illustrate various aspects of the
theory. An intuitive approach which emphasizes the ideas behind the
constructions is complemented by a large number of examples and
figures which both use and support the reader's geometric
imagination.
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 Thurston geometrization
program, leading to the solution of many difficult problems. A
strong effort has been made to point out new connections and
perspectives in the field and to illustrate various aspects of the
theory. An intuitive approach which emphasizes the ideas behind the
constructions is complemented by a large number of examples and
figures which both use and support the reader's geometric
imagination.