Author: Jose M. Montesinos-Amilibia
Publisher: Springer Science & Business Media
This unusual book, richly illustrated with 19 colour plates and about 250 line drawings, explores the relationship between classical tessellations and3-manifolds. In his original entertaining style with numerous exercises and problems, the author provides graduate students with a source of geomerical insight to low-dimensional topology, while researchers in this field will find here an account of a theory that is on the one hand known tothem but here is presented in a very different framework.
Author: Danny Calegari
Publisher: Oxford University Press
This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.
Author: S Kojima,Y Matsumoto,K Saito,M Seppälä
Publisher: World Scientific
This proceedings is a collection of articles on Topology and Teichmüller Spaces. Special emphasis is being put on the universal Teichmüller space, the topology of moduli of algebraic curves, the space of representations of discrete groups, Kleinian groups and Dehn filling deformations, the geometry of Riemann surfaces, and some related topics. Contents: Mr Toyosaburo Taniguchi and the Taniguchi Foundation (S Murakami)Computing on Riemann Surfaces (P Buser & M Seppälä)Volumes and Chern–Simon Invariants of Cyclic Coverings Over Rational Knots (H M Hilden et al.)An Estimate of the Number of Non Constant Holomorphic Maps Between Riemann Surfaces (Y Imayoshi)An Infinitesimal Approach to the Stable Cohomology of the Moduli of Riemann Surfaces (N Kawazumi)Deformations of Hyperbolic Cone Manifolds (S P Kerchoff)Nonsingular Parts of Hyperbolic 3-Cone-Manifolds (S Kojima)Lefschetz Fibrations of Genus Two — A Topological Approach (Y Matsumoto)A Geometric Approach to the Complex of Curves on a Surface (Y Minsky)A Linear Representation of the Mapping Class Group of Orientable Surfaces and Characteristic Classes of Surface Bundles (S Morita)Mathematics In and Out of String Theory (S Nag)Parabolization of Elements of Kleinian Groups (K Ohshika)The Simplicial Compactification of Riemann's Moduli Space (R C Penner)Character Variety of Representations of a Finitely Generated Group in SL2 (K Saito)The Third Bounded Cohomology and Kleinian Groups (T Soma)Bloch Topology of the Universal Teichmüller Space (M Taniguchi)and other papers Readership: Mathematicians.
An Introduction in 2 and 3 Dimensions
Author: Albert Marden
Publisher: Cambridge University Press
Over the past three decades there has been a total revolution in the classic branch of mathematics called 3-dimensional topology, namely the discovery that most solid 3-dimensional shapes are hyperbolic 3-manifolds. This book introduces and explains hyperbolic geometry and hyperbolic 3- and 2-dimensional manifolds in the first two chapters and then goes on to develop the subject. The author discusses the profound discoveries of the astonishing features of these 3-manifolds, helping the reader to understand them without going into long, detailed formal proofs. The book is heavily illustrated with pictures, mostly in color, that help explain the manifold properties described in the text. Each chapter ends with a set of exercises and explorations that both challenge the reader to prove assertions made in the text, and suggest further topics to explore that bring additional insight. There is an extensive index and bibliography.
Author: Joel H. Shapiro
Publisher: Springer Verlag
The study of composition operators forges links between fundamental properties of linear operators and beautiful results from the classical theory of analytic functions. This book provides a self-contained introduction to both the subject and its function-theoretic underpinnings. The development is geometrically motivated, and accessible to anyone who has studied basic graduate-level real and complex analysis. The work explores how operator-theoretic issues such as boundedness, compactness, and cyclicity evolve - in the setting of composition operators on the Hilbert space H2 into questions about subordination, value distribution, angular derivatives, iteration, and functional equations. Each of these classical topics is developed fully, and particular attention is paid to their common geometric heritage as descendants of the Schwarz Lemma.
Author: George Jennings
This is an introduction to the theory and applications of modern geometry. It differs from other books in its field in its emphasis on applications and its discussion of Special Relativity as a major example of a non-Euclidean geometry. Besides Special Relativity, it covers two other important areas of non-Euclidean geometry: spherical geometry (used in navigation and astronomy) and projective geometry (used in art). In addition, it reviews many useful topics from Euclidean geometry, emphasizing transformations, and includes a chapter on conics and planetary orbits. Applications are stressed throughout the book. Every topic is motivated by an application and many additional applications are given in the exercises. The book would be an excellent introduction to higher geometry for those students, especially prospective mathematics teachers, who need to know how geometry is used in addition to its formal theory.