Classical Aspherical Manifolds (Cbms Regional Conference by F. Thomas Farrell and L. Edwin Jones

By F. Thomas Farrell and L. Edwin Jones

Aspherical manifolds--those whose common covers are contractible--arise classically in lots of parts of arithmetic. They happen in Lie workforce concept as definite double coset areas and in man made geometry because the area types protecting the geometry. This quantity comprises lectures introduced by way of the 1st writer at an NSF-CBMS nearby convention on K-Theory and Dynamics, held in Gainesville, Florida in January, 1989. The lectures have been essentially involved in the matter of topologically characterizing classical aspherical manifolds. This challenge has for the main half been solved, however the three- and four-dimensional instances stay an important open questions; Poincare's conjecture is heavily with regards to the three-dimensional challenge. one of many major effects is closed aspherical manifold (of size $\neq$ three or four) is a hyperbolic area if and provided that its basic workforce is isomorphic to a discrete, cocompact subgroup of the Lie crew $O(n,1;{\mathbb R})$. one of many book's topics is how the dynamics of the geodesic circulate might be mixed with topological keep an eye on thought to check safely discontinuous staff activities on $R^n$. the various extra technical issues of the lectures were deleted, and a few extra effects acquired because the convention are mentioned in an epilogue. The publication calls for a few familiarity with the fabric contained in a simple, graduate-level path in algebraic and differential topology, in addition to a few undemanding differential geometry.

Show description

Read or Download Classical Aspherical Manifolds (Cbms Regional Conference Series in Mathematics) PDF

Similar science & mathematics books

Surveys in Modern Mathematics

This selection of articles from the self sustaining college of Moscow is derived from the Globus seminars held there. they're given via global professionals, from Russia and in other places, in numerous components of arithmetic and are designed to introduce graduate scholars to a couple of the main dynamic components of mathematical examine.

Quaternion orders, quadratic forms, and Shimura curves

Shimura curves are a far-reaching generalization of the classical modular curves. They lie on the crossroads of many parts, together with advanced research, hyperbolic geometry, algebraic geometry, algebra, and mathematics. This monograph offers Shimura curves from a theoretical and algorithmic standpoint.

Narrative Approaches to the International Mathematical Problems

This e-book units itself except such a lot, if now not all, the opposite books since it deals narrative research and suggestions to a number of the world's hardest mathematical difficulties utilized in the foreign and nationwide competitions around the world. on the time of this book's e-book, options to a lot of those difficulties had now not been came across at any place.

Additional info for Classical Aspherical Manifolds (Cbms Regional Conference Series in Mathematics)

Example text

Hdt. ^.. s r.

V n} : F(V) v 6 V vector weaker: from over a vector to be a given to t h e s e V : Vp ~ V q . T something of for bundle "parallel" seems a curve concept So and is a d i f f e r e n t i a b l e v 6 V Therefore p,q this the a differentiable vector isomorphism bundle associate translate T M of corresponding along let will v t 6 Vy(t), V the ~ M bundle points from manifold. a real is p o s s i b l e : [a,b] "connection" space of translation suppose parallel Given require What parallel y(b) we tangent a trivial requirement.

W h i t n e y ) . an isomorphism I : A*(S) ~ C*(S) in h o m o l o g y . 18) I o E = id, E : C*(S) ~ A~(S) ~ Ak-1(S), ~ o I, and n a t u r a l k = 1,2 .... , such chain that E 0 ~ = d o E E o I - id = Sk+ I o d + d o s k, k =0,1,... For the p r o o f we f i r s t usual Ap c ~p+1 is the s t a n d a r d = canonical basis coordinates respect {e0, .... ,tp). 2. 21) and t h e r e f o r e satisfy i,j by the is star s h a p e d w i t h (of. E x e r c i s e (j)d~ + d h ( j ) ~ For Ap j = 0 ..... p, ~ 6 A0(&P) .

Download PDF sample

Rated 4.25 of 5 – based on 8 votes