Geometry of crystallographic groups [[electronic resource] /] / Andrzej Szczepański

• Record Nr.: UNINA9910785918503321
• Autore: Szczepański Andrzej
• Pubbl/distr/stampa: Hackensack, NJ, : World Scientific, 2012
• ISBN: 1-283-63598-4; 981-4412-26-0
• Descrizione fisica: 1 online resource (208 p.)
• Collana: Algebra and discrete mathematics ; ; v. 4
• Disciplina: 548/.81
• Soggetti: Symmetry groups; Crystallography, Mathematical
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Contents; Preface; 1. Definitions; 1.1 Exercises; 2. Bieberbach Theorems; 2.1 The first Bieberbach Theorem; 2.2 Proof of the second Bieberbach Theorem; 2.2.1 Cohomology group language; 2.3 Proof of the third Bieberbach Theorem; 2.4 Exercises; 3. Classification Methods; 3.1 Three methods of classification; 3.1.1 The methods of Calabi and Auslander-Vasquez; 3.2 Classification in dimension two; 3.3 Platycosms; 3.4 Exercises; 4. Flat Manifolds with b1 = 0; 4.1 Examples of (non)primitive groups; 4.2 Minimal dimension; 4.3 Exercises; 5. Outer Automorphism Groups; 5.1 Some representation theory and 9-diagrams5.2 Infinity of outer automorphism group; 5.3 R1 - groups; 5.4 Exercises; 6. Spin Structures and Dirac Operator; 6.1 Spin(n) group; 6.2 Vector bundles; 6.3 Spin structure; 6.3.1 Case of cyclic holonomy; 6.4 The Dirac operator; 6.5 Exercises; 7. Flat Manifolds with Complex Structures; 7.1 Kahler flat manifolds in low dimensions; 7.2 The Hodge diamond for Kahler flat manifolds; 7.3 Exercises; 8. Crystallographic Groups as Isometries of Hn; 8.1 Hyperbolic space Hn; 8.2 Exercises; 9. Hantzsche-Wendt Groups; 9.1 Definitions; 9.2 Non-oriented GHW groups; 9.3 Graph connecting GHW manifolds9.4 Abelianization of HW group; 9.5 Relation with Fibonacci groups; 9.6 An invariant of GHW; 9.7 Complex Hantzsche-Wendt manifolds; 9.8 Exercises; 10. Open Problems; 10.1 The classification problems; 10.2 The Anosov relation ; for flat manifolds; 10.3 Generalized Hantzsche-Wendt flat manifolds; 10.4 Flat manifolds and other geometries; 10.5 The Auslander conjecture; Appendix A Alternative Proof of Bieberbach Theorem; Appendix B Burnside Transfer Theorem; Appendix C Example of a Flat Manifold without Symmetry; Bibliography; Index
• Sommario/riassunto: Crystallographic groups are groups which act in a nice way and via isometries on some n-dimensional Euclidean space. They got their name, because in three dimensions they occur as the symmetry groups of a crystal (which we imagine to extend to infinity in all directions). The book is divided into two parts. In the first part, the basic theory of crystallographic groups is developed from the very beginning, while in the second part, more advanced and more recent topics are discussed. So the first part of the book should be usable as a textbook, while the second part is more interesting to resea

Connections [[electronic resource] ] : an introduction to the economics of networks / / Sanjeev Goyal

• Record Nr.: UNINA9910792397703321
• Autore: Goyal Sanjeev
• Pubbl/distr/stampa: Princeton, N.J. ; ; Oxford, : Princeton University Press, c2007
• ISBN: 1-282-93555-0; 1-282-45819-1; 9786612935558; 0-691-14118-5; 9786612458194; 1-4008-2916-X; 0-691-12650-X
• Edizione: [Course Book]
• Descrizione fisica: 1 online resource (302 p.)
• Classificazione: 83.01
• Disciplina: 330.0151
• Soggetti: Economics, Mathematical; Social networks - Economic aspects; Social networks - Mathematical models
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographic references and index.
• Nota di contenuto: Front matter -- Contents -- Acknowledgements -- 1. Introduction -- 2. Networks: Concepts And Empirics -- 3. Games On Networks -- 4. Coordination And Cooperation -- 5. Social Learning -- 6. Social Networks In Labor Markets -- 7. Strategic Network Formation: Concepts -- 8. One-Sided Link Formation -- 9. Two-Sided Link Formation -- 10. Research Collaboration Among Firms -- References -- Index
• Sommario/riassunto: Networks pervade social and economic life, and they play a prominent role in explaining a huge variety of social and economic phenomena. Standard economic theory did not give much credit to the role of networks until the early 1990's, but since then the study of the theory of networks has blossomed. At the heart of this research is the idea that the pattern of connections between individual rational agents shapes their actions and determines their rewards. The importance of connections has in turn motivated the study of the very processes by which networks are formed. In Connections, Sanjeev Goyal puts contemporary thinking about networks and economic activity into context. He develops a general framework within which this body of research can be located. In the first part of the book he demonstrates that location in a network has significant effects on individual rewards and that, given this, it is natural that individuals will seek to form connections to move the network in their favor. This idea motivates the second part of the book, which develops a general theory of network formation founded on individual incentives. Goyal assesses the robustness of current research findings and identifies the substantive open questions. Written in a style that combines simple examples with formal models and complete mathematical proofs, Connections is a concise and self-contained treatment of the economic theory of networks, one that should become the natural source of reference for graduate students in economics and related disciplines.