Spherical CR Geometry and Dehn Surgery by Richard Evan Schwartz

By Richard Evan Schwartz

This publication proves an analogue of William Thurston's celebrated hyperbolic Dehn surgical procedure theorem within the context of advanced hyperbolic discrete teams, after which derives major geometric effects from it. the 1st is the development of huge numbers of closed genuine hyperbolic 3-manifolds which certain complicated hyperbolic orbifolds - the one identified examples of closed manifolds that at the same time have those different types of geometric buildings. the second one is a whole knowing of the constitution of complicated hyperbolic mirrored image triangle teams in instances the place the attitude is small. In an obtainable and simple demeanour, Richard Evan Schwartz additionally provides a large number of necessary details on advanced hyperbolic geometry and discrete groups.Schwartz depends upon common proofs and avoids quotations of preexisting technical fabric up to attainable. consequently, this publication will profit graduate scholars looking access into this rising region of study, in addition to researchers in allied fields equivalent to Kleinian teams and CR geometry.

Show description

Read Online or Download Spherical CR Geometry and Dehn Surgery PDF

Similar differential geometry books

Minimal surfaces and Teichmuller theory

The notes from a collection of lectures writer added at nationwide Tsing-Hua collage in Hsinchu, Taiwan, within the spring of 1992. This notes is the a part of ebook "Thing Hua Lectures on Geometry and Analisys".

Complex, contact and symmetric manifolds: In honor of L. Vanhecke

This e-book is targeted at the interrelations among the curvature and the geometry of Riemannian manifolds. It comprises examine and survey articles according to the most talks added on the foreign Congress

Differential Geometry and the Calculus of Variations

During this publication, we research theoretical and useful facets of computing tools for mathematical modelling of nonlinear platforms. a few computing ideas are thought of, akin to equipment of operator approximation with any given accuracy; operator interpolation thoughts together with a non-Lagrange interpolation; equipment of procedure illustration topic to constraints linked to options of causality, reminiscence and stationarity; equipment of process illustration with an accuracy that's the most sensible inside a given classification of types; equipment of covariance matrix estimation;methods for low-rank matrix approximations; hybrid equipment in response to a mixture of iterative approaches and most sensible operator approximation; andmethods for info compression and filtering less than situation clear out version may still fulfill regulations linked to causality and kinds of reminiscence.

Extra info for Spherical CR Geometry and Dehn Surgery

Sample text

3, the term perturbation means that there is a single > 0 so that all partial derivatives of Fj are within of the corresponding partial derivatives of Ej . 3 has two cases, which we will establish in turn. 1 Case 1 Suppose that k ≥ n + 2. ,ck ) ∈ Rk and y ∈ V , define Θ(c, y) = E1 (y) + c1 , . . , Ek (y) + ck . Here Θ is a map from Rk × V to Rk . ,1). The linear differential dΘ is clearly a surjection at each point. Hence, Θ−1 (L) is (n + k) − k + 1 = n + 1 dimensional. Since k ≥ n + 2, the projection of Θ−1 (L) into Rk must avoid points of Rk that are arbitrarily close to 0.

210–214]. Given 3 points a, b, c ∈ S 3 , we take lifts a, b, c ∈ C 2,1 and consider the triple a, b, c = a, b b, c c, a ∈ C. 22) It turns out that this quantity always has negative real part and changing the lifts multiplies the number by a positive real constant. 23) 2 2 is independent of lifts and is P U (2, 1)-invariant. This invariant is known as the Cartan angular invariant . It turns out that A = ± π/2 iff the points all lie in a C-circle and A = 0 iff the points all lie in an R-circle. In general, two triples (a1 , b1 , c1 ) and (a2 , b2 , c2 ) are P U (2, 1)-equivalent iff they have the same angular invariant.

Bk ) ∈ (Rn )k , and y ∈ V , we define Θ(a, b, y) = (F1 , . . , Fk , G1 , . . , Gk ), monograph August 20, 2006 27 TOPOLOGICAL GENERALITIES Fj (y) = Ej (y) + aj + bj · y, Gj (y) = ∇Ej (y) + bj . 4) RB = Rk × Rnk . 5) Note that ∇Fj = Gj . The map Θ is a smooth map from an open subset of RA into RB , where RA = Rk × Rnk × Rn , Consider dΘz at some point z ∈ V . • By varying just the a coordinates, we see that the image of dΘz contains Rk × {0} ⊂ RB . • Let π : RB → Rnk be the projection onto the last nk coordinates.

Download PDF sample

Rated 4.28 of 5 – based on 21 votes